DVD MOVIE: Not a problem, technically, in that PS3 was already known to not feature upscaling in this mode -- it's still enough to piss a person off, but when you went to the store, you already knew it wouldn't have that feature. Will play in 480p.
PS2/PS1 GAME: Not a problem, just a bummer (same situation as DVD). Will play in 480i/p, as expected since PS3 currently doesn't do any scaling.
AVC/MPEG1/MPEG2 VIDEO: Not a problem. Downloaded or personally encoded videos will run at whatever the TV is set at, even if the original file uses an immense 1080p encoding size. And surprisingly, the TV or PS3 does not need to reset any setting to play video files at any resolution.
PS3 XMB MENU: Not a problem. The PS3 will output to 480i/p, 720p, 1080i, or 1080p. The only issue that might arise would be if you somehow already have your PS3 set for 720p, in which case the signal will not be initially compatible with your 1080i TV and will display fuzz. To remedy this, hold down the Power button on PS3 until it beeps twice (once for shutdown, once for resetting the video setting), at which point it will boot in 480i (which works on every TV) and then you can go back in and switch to 1080i.
BLU-RAY MOVIE: Possibly a problem. Will run in 1080i (making it save for those with the 1080i-only problem), but may not run in 720p. The maximum PS3 of the PS3 in Blu-Ray mode is the encoded movie's native 1080p. If you set your PS3 to 1080i, the system will run a refresh setting sequence (for reasons unknown, as it never switches video settings to our knowledge) and then it will come back on in 1080i mode to play the movie at that resolution. If you set your PS3 to 720p, reports are saying that it will switch to either 1080i or 480p to play the movie.
PS3 GAME: Problem. If your HDTV has 1080i support but not 720p support, you will not get 1080i out of games that do not fit it. Your 1080i-only HDTV will not accept the 720p signal and the game will kick down to 480p mode. As mentioned, it will not scale up to 1080i. Please check your HDTV manual or the manufacturer's website to see if your HDTV is affected by this limitation.