Valve seems to be giving away invitations to the closed beta of the Steam Mobile beta like candy, so when I downloaded the app and tried to log in (how to ask for an invite) I found a nice new inventory item in my account when I got home - another invite! Which means I got in!
As a quick side note, I think it's hilarious that they give you an additional invite in your inventory as a tradable item. I had a friend who was going to offer me his for my iPod headphones accessory for TF2. He was bummed when I arrived home to find that I had an invite of my own! It was a happy ending though - I offered them to him for free and ended up walking away with 50% off a Valve game from the Christmas special challenges.
So, the Steam Mobile application. It is awesome, my friends. You can browse the store, add games to your wishlist, buy games, check out the community page, profiles, chat with your friends...pretty much the only thing you can't do with it is play any actual games.
The chat works and looks great. I only had one small problem with it where you get about 2 - 5 seconds lag after you press send before it actually sends the message; connecting to wifi helped the issue but I still noticed a lag. However, it seems to make up for this a little by showing a "..." while someone is typing. So even if there's a lag after someone presses send you can still see that they are about to say something.
Surprisingly, I didn't notice a horrible battery drain. Yes, it's going to take a toll as any running application would, but I expected it to do a lot more damage to my power than it did for how great it looks. Unless you purposefully exit you'll notice that a Steam icon remains in your notification bar to remind you it's running.
Overall I was pretty impressed with the whole thing. I'm excited to have my Steam chat list available to me when I'm away from the computer because I definitely have people who I am friends with on Steam that I don't have connections with elsewhere. Plus you gotta love Valve for giving us another convenient way to shovel our money at them - and shovel I shall!
Valve is built on a great community and this is a fantastic extension of that. So download the application for either Android or iOS and go for the closed beta invite (be sure to try and log in so they add you to the list - this includes putting in a secure code they send you in email when you log in from a new computer)! Even if you don't get in, there's a good chance you'll be able to trade one of your TF2 hats for one!