Hello,
It sounds like your problem is caused by something called overscan. On most tv's the picture you see is actually zoomed in slightly, cutting off a small amount from the top, bottom and sides of the picture. This is used to cover up most of the rubbish normally hidden at the side of the picture such as timing and registration marks.
On modern High Definition TV's, it is possible to turn overscan off, and to view the entire picture - normally this is not a problem as most modern programming is quite tidy in these missing areas (apart from the occasional white bars at the top of the picture) This also allows High Definition pictures to be placed correctly on the screen for the best quality.
Chances are that overscan is turned off on your television and is showing the 'messy' edges from your old VHS tapes.
Consult your manual as this setting is in different places on different TV's. On samsung TV's for example - it is called Just Scan and is an option on the aspect menu. On panasonic TV's it is in the TV setup menu and is called picture overscan.
Hope that helps.
Chris