I know this is an older thread, but let me add from my experiences recently.
I recently decided to move my PS3 into my gaming room (PC room) since I primarily spend most of my time on PC. I wanted to run my PS3 to play with friends from work on the same monitor as my PC to make it easy to go back and forth and since my Wife hogs the nice 60" in the living room and I can't stand controllers for shooters (mouse and keyboard guy) I started looking for a monitor to run both on.
All that said here is what I found. Computer LCD displays while better than your average LCD TV do not have TV tuners or a Scaler built in. Unlike the Xbox360, which does have a built in hardware scaler, the PS3 does not have the ability to scale a 720P game up to 1080I or 1080P resolution.
Because a PC monitor (LCD) runs at a native 1920x1080 resolution and 16:9 you get a 720P picture stretched out to fill a 1080P screen. This makes games on the PS3 in 720P like BF3 looked fuzzy, blurred, and pixelated not to mention the aliasing effect on edges is horrible.
What you have to do if you want the PS3 games that run in 720p to look halfway decent (which compared to the native 1080P res on PCs is a huge step down) is get a PC monitor that has a built in scaler or look for a LCD TV with a 5ms response time or lower that has PC connections.
After finding out the hard way that the PS3 will not convert to 1080P like the Xbox I ended up going back and getting a 27" HDTV with DVI and HDMI hookups. I would have gone with a 32", but sitting as close as I do 32" was too much. 27" seems to be perfect when sitting a couple feet back.
I'm used to playing BF3 on the PC at high res so there is no way the dumbed down graphics of the PS3 version will ever look as good no matter what you do, but at least the screen I have now will scale on it's own so everything does not look washed out.
When people say their PS3 games look horrible on their computer monitor 9 times out of 10 this is the reason. Make sure the screen you are using has a scaler built in to run any resolution not just 1080p.