While Civilization 5 does many things right, such as the wonderful hex's, no stack-of-doom, etc -- there are an astounding amount of issues that are a complete step back for the series. It becomes more and more obvious the more one plays Civ 5, that this game could have used more time in the oven. It seems the interest in this game is taking a sky-dive on various forums, it really doesn't bode well for the game's life-span.
Needless to say, this game is terribly disappointing...only because it has so much potential!
I'm writing this as I play a normal game, because there are just so many issues with this thing! I'm going to put what I think are the biggest issues in bold.
   

• Beakers (research points/science) do not overflow into the next technology for your civilization, resulting in tons of wasted points over the course of a game.  Take note, Civilization 4 did this fine.  The only counter to this is to (tediously) micro-manage specialists/focus in your cities to try to reduce how many beakers are wasted on the last turn of research. This is not sheduled to be fixed in a patch or is even mentioned by Firaxis Games, yet is one of the biggest GLARING issues right-now...Perhaps the biggest slap-in-the-face is this is a trivial thing to fix programming-wise!
  

• You can't raze the capital cities you've taken over -- for no reason what-so-ever. [ANGRY FACE] Simply infuriating considering puppet state AI + Unhappy points that are generated!

• Unit up-keep costs are seemingly exponential and terribly limiting. Does the game want me to keep an army to defend myself (and go bankrupt!!!) or does it want me to have gold and be taken over by the civ next-door? Bad game design....

•  Multiplayer is Nigh - unplayable. Crashes, bugs, and bad times all around...How did this game ship like this!?

•  Puppet state AI builds civilization and coffer draining buildings such as stables, granaries, and so-forth. You might as well raze any city your allowed to.   

• Box-o'-rocks computer AI makes even the worst player look like an Einstein.  They will toss any unit at your city to get destroyed. After the first patch the AI has gotten better about this, but not by much. :/
• You can grab a city-states or civ's workers on the same turn you declare war, then you can make peace a turn later. Free workers!  
• The computer can (on a  blue moon) accidentally stack 2 different military units together on the same tile. REALLY? What sloppy coding...in this case it was a Siam elephant and a rifleman.
• Why can India and Siam produce totally-sick elephant units (these are some of the best units in the game...) with tons of power without even needing an ivory source(elephants) to produce them? This kind-of predisposes them to dominating every other AI very early on....(then stomping you...)
  
• Killing a few of an AI civ's units will result in them forking over a large sum of gold for a 10 turn peace treaty, then you can rinse and repeat later for more cash.  
• AI's will ask you for all your possessions if you are at war with them (if they started war) for 10 turns of peace, even if your kicking their ass. What?
  
• AI's will (seemingly at random) flip-out on you, declaring war and calling you a warmonger, even if you've never attacked anyone and have been best of friends forever. After this, the other civ's in the game will follow suit and before you know it, the entire world wants you dead.  
• Dragging a path for a unit to travel over a few turns might result in the unit wasting movement points along the way or when they reach the end of  the destination. The game will not alert you that the unit is done moving, and needs orders.
• AI players can attack or move with a bought military unit the turn it is produced, for players, they cannot.  
• Research agreements with AI's will hardly (if-ever) complete or get lost for no reason, even if you don't declare war on the AI you signed with. 250 gold down the drain, every-time. 
• You can't trade tech's with civ's like in previous games in the franchise. Was this some sort of bizarre game design decision? Why? It feels so limiting.
• Tedious load times, especially when first starting the game up -- you are forced to watch the intro movie while the game loads...something. Does it really take this long to load a few menus and such? After this, you have to wait for the main game to load after you have set up a game...really? 
• There is hardly any way to tell what kind of reputation you have with a AI Civ unless they are blatantly angry with you, just met you, or are pleased with you. Civilization 4 gave you a point list of why an AI behaves to you the way they do. 
• Victory screen has doesn't have the in-depth map or graphs that show you over time what happened during the course of the game. Civ 4 already had this. All you get is some paltry charts and demographics. Anti-climactic much? Before the first patch, it didn't even have the "just...one..more...turn" button! 
• AI will CONSTANTLY bother you over diplomatic matters in the mid/late game. There is no way to turn this off -- terribly annoying. Almost every turn the AI is asking me for something or just taunting me  (despite I could flatten them into the earth in a couple turns...)  for no reason. Again...why? 
• AI will tend-to not accept peace or give gold/resources for peace, even if they are on the verge of losing their last city in a few turns to the player, if the player asks them for peace. Okay duder, it's YOUR empire...I guess they have some semblance of dignity?
• Many buildings/city improvements are completely worthless and probably even detrimental to your city/civ, as they cost WAY too much maintenance gold for their worth...
• AI's tend to go ONLY for domination victory and/or space victory. On average...