The big "How do I choose an HDTV?" thread.

Theoretically, nothing. It's mainly a weight thing. At any given moment in time a larger TV would be heavier.

If, however, the new TV is no heavier than the maximum rated weight for the stand, then you should be fine.

At some point the larger TV might be too big as there looks to be a fixed vertical clearance, but I'd expect that to only become an issue once the TV is over 100".

Assuming your stand uses VESA mounts, check to make sure that the larger TV has a compatibly-sized set of VESA holes.

As a guy who does AV work professionally the size thing is mostly BS for mounting as weight is the more important factor. You will also want to compare the size of the VESA mounting plate of your stand to the size that the newer TV uses. There are some adapter plates you can get that will let you adapt say a 75mm x 75mm plate to work with a 200mm x 200mm mount. Samsung for instance generally uses a 400mm x 400mm VESA plate for their TVs 65 inches and up. The fun part is you will often need to dig through the TV manual to figure out what size of VESA mount they actually use as they usually just list them as VESA Compatible on the product pages.

Okay, cool, that makes sense. Really good information to have. Thanks all!

The only way I've found size to be a factor is in the weight distribution. I have a monitor arm that claims up to 15lbs but only 27" in screen size. I put a 32" monitor on it that weighs under 15lbs and it mostly works, but I am unable to tilt it forward, as it immediately tilts all the way unless it's perfectly straight up. So I think this may happen because more of the weight is distributed further from the mounting point than it would be if it were a 27 inch monitor.

This is with a fully articulated gas spring arm, so less articulated mounts might not have this issue.

Even though the store mounted our 65" tv themselves, and guaranteed their work, and the tv, it still freaked me out to swivel the tv away from the wall.

Now, it's normally nowhere near the wall, and at quite an angle if I'm watching it from my recliner chair.
Weird how you get used to things.

This random image I found pretty much covers our before/after:

I use these at work. When mounted properly you can hang an overweight 42 year old off of them We used to hand these heavy as hell 85 inch Sharp multi-touch displays with them.

I did go with a slightly cheaper option at home though. I don't like the models with only a single support arm, I have seen them fail.