Yesterday, me and my friends did a six-hour marathon in Coin-op mode in The Second Encounter. Little did we know that the achievement for completing that mode is FUCKING BROKEN. We got nothing. And we got other achies on the way to the finish so Steam was working fine.
So no more new secret locations until they figure this shit out. I'm done.

This third level only has one new secret. to get it, you must destroy all four double-headed snake statues you find while going through the level. The first couple of them are on the top of some doors you have to go through, another one is in the little hut that contains the "spanish cannon" secret, and the final one is just before the underground installation. When you blast the final statue, a big teleport will appear in front of it, that will take you to a room with a huge double-headed snake. Take the items you find there quickly cause you'll be teleported out a few seconds later.

This level has 9 secrets instead of 8, but the ninth one is the well-known Invulneravility on the rock ledge, that didn't count as a secret in the old Second Encounter due to a glitch.

The old SS:TSE had 12 secrets on the first level. The HD version has 15. These are the 3 new ones.
First one: You know that "Hall of Fame" room where the big-head devs show up? Theres a tree outside it.
 Cut it down, and a Tommy gun will appear outside the room with the sniper rifle.
The other two new secrets are 2 ammo boxes that appear to each side of the Tommy gun. To get them, just keep cutting trees around the place the gun appeared. At first I though it was a specific tree I had to cut down, but as i tried different ones I came to the conclusion you need to cut down 2-3 trees for each box to appear. Which ones you cut, it doesn't matter.
 
I will continue updating if I find any new secrets that aren't on the old Second Encounter.

Just trying out the Blog feature. I will update as the time goes.
This week I will attempt the Serious Sam HD: The Second Encounter speedrun as well as other single plyer and co-op achievements. Hope to get the S-Ranking!