First off, screen size, in and of itself, has nothing to do with the problem; the problem is resolution! It just so happens that newer, bigger monitors tend to come with their default resolution set higher than the maximum possible for older machines. You can usually set your newer monitors to a lower resolution than they're set at, from the factory, and possibly find common ground among all the machines involved, here. The higher resolutions offered, especially on larger monitors, are great if you're dealing with commercial graphics programs...or playing advanced video games...but are really overkill for most business applications, such as running databases.
There are hacks out there for adjusting the size of Forms (some for free, some for a fee) based on the resolution of the machine they're running on, but all of these come with the same caveat, as Ajax touched on; they all only perform well when the programs are developed in the lowest resolution you're likely to encounter!
Using the lowest common denominator, in program development, is pretty much always the best policy! You can't, for interest, develop a database in Access 2010, using features just introduced in that version, and expect to run the app on a machine running Access 2003, can you?
Here's a link to one of these hacks that has been around for a very long time and has a good reputation:
ShrinkerStretcher
Linq ;0)>
The problem with making anything foolproof...is that fools are so darn ingenious!
All posts/responses based on Access 2003/2007