I think the "jank" that bothers people so much is in there by design. 
 
To start off, the main enemies you'll face are zombies. Zombies of the slow-moving variety. We all recognize how silly it is for a human to be afraid of a slow shuffling zombie because the human is moving at full speed. Thus slow-moving zombies come in numbers, to apply suffocating pressure on the protoganist. Developing that sense of pressure is what drives many of the choices they've made. They want to build some desperation.
 
1) If you are too capable, that kind of suffocation becomes impossible. To illustrate with an extreme example, imagine Ryu from Ninja Gaiden trucking through fortune city or willamette mall. Hardly a fair fight, he'd just wall run right over them, or slice through dozens in a single swing. There's no balance.  Then there's the excessively agile and powerful psychopaths. They're a direct contrast to the slow and weak zombies. Unfortunately, they need to balance the protagonist capabilities against both enemy types. Since they can't put the player at slow and fast speeds, they design the psychopaths as combat puzzles to give them period of exposure for the slow-moving player to catch up. 
 
2) To add to the feeling of suffocation, you're on the clock...all the damn time! It's frustrating! Since you're swimming through hordes of zombies, they provide a relatively low level of danger. Given enough time, you could cautiously pick off the shuffling mob in safety. The time limit forces you to take risks with your player's health and the survivors along with him. You have to grab multiple survivors in each run because of the time limit if you want to protect them all, without a timelimit you'd only need to do one at a time.
 
3) The limited save and restart system ties in as well to providing pressure on the player. It provides high difficulty to all players at first (note that there's no difficulty selection), but given enough restarts, the challenge scales down to where any player will get through eventually. In the end, you're awesome. After struggling early on, you're a beast by the end and you appreciate it that much more because you can see how far you've grown. The player doesn't just take satisfaction in their accrual of power, but they also accrue experience. On my first run in Dead Rising, I was forced to restart by case 3 and finished it on the second playthrough. Months later I came back on a fresh run starting at level 1 and finished all the side missions on the first pass. The game gives the player opportunity to improve at handling its challenges, and that improvement gives satisfaction, its separate from the leveling. 
 
4) Lack of free roam. They don't let you just go finding secrets and level up without any pressure. This would allow players to circumvent much of the challenge and blow through the main game. Players do not always play the game in the most enjoyable way, this is especially evident in MMOs where players bypass content because they can grind a random spawn that gives too much XP. If the fastest way for the player to level up is to click a firehydrant for hours at a time, that's how players will play. The designer needs to make the fastest way to level match with the most fun way to play. Even exploring in free roam without PP carrying over would still give the player a big advantage in navigating DR1&2's challenges. Getting through the mall by exploiting its resources is part of the gameplay. 
  
 I think developers should always look at their design and ask "Is it fun?" and allow that to inform their decisions. I think in this case, they decided that it'd be more fun to have more pressure rather than less. 

To be clear here : I'm just saying that the clunkiness is probably intentional; just part of their design choices. This does not excuse them from criticism of course. I'm not saying they were good choices and I don't agree with all of them.
I don't think DR1&2 suffer from a lack of polish or consideration (which creates what I'd consider to be "jank"), but rather a series of controversial design choices. What I WOULD consider to be "jank" was DR1's missing text support for non-HD TVs. 

The only thing I hate about the games design and gameplay is how so unfitting it is against the psychopaths. Barely any of your melee attacks are useful and most weapons don't do nearly as much damage as you'd expect ala the Bambow.  
 
I wish they could of changed up the way game plays specifically for that boss; 
 

There's no time to stop and smell the roses. The DR series is a faced paced, stress filled romp through zombie infested areas. You have to keep moving and watch the clock. It's a unique gaming experience. You want to play it one way but you're forced to play it another. It's a sandbox full of snakes. You can't just sit there and goof around. 

Dead rising 2 is a demanding but satisfying experience but one you have to discover.

True, I believe most people have a good understanding of these design choices and implementation if you have any experience with the Dead Rising series. But it is like Abyssfull these choices fall apart when it comes to the high contrast points with the boss battles, psycopaths, and  etc. The boss are just frustrating when you are fighting with a dude on rollerskates and flamethrowers and has no problem getting around the environment. In theory they should be a combat puzzles but it really comes down to a war of attrition (gather enough resources to push through) or just glitch the a.i. Yes you wait for that time to hit them but you will most likely take some damage depending on how slow your attack animation is. 
 
The progression of your character seems less impactful in this version. Yes the running, health, and inventory are a easier way to get around but nothing gives you extra choices while playing the game like the Zombie head walk and etc. in this first one. It is easier to craft weapons and what not but really if you are going through the game it is nail bat, light saber, and boss weapons. 
 
The over all flow of the game is questionable. Going through the environment is not that hard even from level 1. You walk around zombies like a shuffling maze, hit them to get to a door, and repeat for point A to B.  Playing through the game for the "quests" is not  very challenging or engaging. It excludes the "selling points" of the series which is killing zombies in numerous ways because attacking zombies takes up time, crafting takes time, finding health takes time, weapons break, and experience is usually to low to care about. 
 
So the flow breaks down to 
Base > Nail Bat > Run Past zombies> Save > hit some zombies>  loading........> find survivor> text dialog (horrible) > hit some zombies >  loading.... >run past zombies> loading..> Base    *Then repeat. 
 
Sprinkle in the before mentioned psycopaths and bosses and you can see where the design becomes flawed. 
 
I am hoping if they come around to Dead Rising 3 that they look at these core design choices and question them. So they can sculpt a a really well designed game and make a step up in the series like Mass Effect 2, and Assassins Creed 2 . I think Blue Castle has it in them, they just need the freedom and time.

It's basically the same as the the Lost Planet 2, and general Japanese design aesthetic, of animation coming before gameplay. I feel though that Dead Rising is the exception to the rule of this being total shit because this is one of the very few games that don't make you the immediate badass so having to constantly consider the animations, the space left in your inventory and so on keep the idea of survival which wouldn't exist due to the disconnect between the player and the game.

Dead Rising is fun except for the psychos it's only then that you realize chuck moves like a fucking tank.

" True, I believe most people have a good understanding of these design choices and implementation if you have any experience with the Dead Rising series. But it is like Abyssfull these choices fall apart when it comes to the high contrast points with the boss battles, psycopaths, and  etc. The boss are just frustrating when you are fighting with a dude on rollerskates and flamethrowers and has no problem getting around the environment. In theory they should be a combat puzzles but it really comes down to a war of attrition (gather enough resources to push through) or just glitch the a.i. Yes you wait for that time to hit them but you will most likely take some damage depending on how slow your attack animation is.   The progression of your character seems less impactful in this version. Yes the running, health, and inventory are a easier way to get around but nothing gives you extra choices while playing the game like the Zombie head walk and etc. in this first one. It is easier to craft weapons and what not but really if you are going through the game it is nail bat, light saber, and boss weapons.    The over all flow of the game is questionable. Going through the environment is not that hard even from level 1. You walk around zombies like a shuffling maze, hit them to get to a door, and repeat for point A to B.  Playing through the game for the "quests" is not  very challenging or engaging. It excludes the "selling points" of the series which is killing zombies in numerous ways because attacking zombies takes up time, crafting takes time, finding health takes time, weapons break, and experience is usually to low to care about.   So the flow breaks down to  Base > Nail Bat > Run Past zombies> Save > hit some zombies>  loading........> find survivor> text dialog (horrible) > hit some zombies >  loading.... >run past zombies> loading..> Base    *Then repeat.   Sprinkle in the before mentioned psycopaths and bosses and you can see where the design becomes flawed.    I am hoping if they come around to Dead Rising 3 that they look at these core design choices and question them. So they can sculpt a a really well designed game and make a step up in the series like Mass Effect 2, and Assassins Creed 2 . I think Blue Castle has it in them, they just need the freedom and time. "

I seriously don't understand why people are having such a hard time with the Psychos.  
 
Just bring a shotgun. 
 

" If the fastest way for the player to level up is to click a firehydrant for hours at a time, that's how players will play.  "

I'm not agreeing or disagreeing with any arguments being posited here. I just want to point something out.  
 
Just because something is deliberate doesn't mean it works.