Biggest problem I had with 360 on SDTV was overscan, used to lose a good couple of cm's of picture either side of the screen, so like on Lost Odyssey you couldn't see the first letter of menu options lol
Worked fine though.
One thing i'll say, if you are running a 360 on an SDTV, GET AN RGB SCART CABLE, the image quality vs the standard Composite cable they ship with it is night and day.
Actually makes text readable, stops all the colour bleed in games with high contrast (like mirrors edge), and generally just makes everything look a million times better.