I've got a couple of old Trintron monitors. A 21" PVM that serves as my daily watcher at the moment and a 12" (forget the model at the moment) that serves as a test monitor/shop set.

The 21" has a great picture except for a red "shadow" around certain images. Similarly the 12" has an excellent picture except that it is a bit trapezoidal rather than rectangular.

How difficult is it to adjust these back to the way they should be?
Hopefully with a the right adjustments these will provide a great picture for years to come.

I remember years ago I tried to adjust the convergance on an old Kriesler delta gun set. I made it a lot worse before I got it any better and it took ages. Admittedly I was doing the adjustments to an off the air picture, and I probably did them in the wrong order. I don't want to repeat that this time. :)

Most Sony's have a pretty complete set of geometry adjustments, even a 21". They will mostly be small pots scattered around the deflection board. Look things like "pin amp", "pin phase" and "keystone", or abbreviations of those names. They function like the controls on a computer monitor. A PVM monitor should have lots and lots of control to play with and should end up with near perfect geometry. A cross hatch generator is a must; don't even start until you have a way to display one. There will be two sets of controls if it supports underscanning, so make sure you adjust the right set. Also, be sure to adjust the geometry after the size and centering because they interact. Most Sonys look a lot better after a little adjustment.

Center convergence is adjusted by the rings on the neck of the CRT and the H Stat control. Edge convergence is adjusted by tilting the yoke. There may be a few pots and coils on the yoke that also affect dynamic convergence.