In the past when doing things like this I've kept everything within one uber-PSD file using layer groups for each 'file', plus a few layer groups for shared elements like headers and background. To switch from 'file' to 'file', I toggle the visibility of the appropriate groups. This avoids your issue being a problem, but it's a bit clunky. You'll want to back that file up often!
I ask because I’m designing an iPhone app and it uses the same modules over and over across different screens. There are dozens of screens and each time I needs to change a button or text field in a module, I need to fix it one at a time in each file. Sucks!
This sounds like a case for Adobe Fireworks and it's Master Pages and States features. In fact, your very problem sounds exactly like this guy's Point 1 in a 10 point list on why he prefers Fireworks to Photoshop for similar tasks (in his case web page knockups rather than apps, but the issues are similar). He says:
When working on a multi-page mock-up for a site design, the advantages
of having all your assets contained within a single file are enormous.
Although having 5 different PSD files may be workable initially, once
edits and changes are required, for example changing text in a
consistent header or footer, things can soon get messy and
time-consuming as changes have to be made across all files.
Unlike Photoshop, Fireworks allows you to set up a "Master page" which acts like a template, containing all the things that are common to all the views in your app, which you can then put specific stuff on top of.
It also has a "States" feature which stores differences with other states. You could use to store and show differences within one app view - for example highlighted and non-highlighted buttons.
No-one likes a "Try a different application" answer, but if you haven't tried Fireworks for knockups for interactive views, it is seriously worth trying. It has loads of benefits beside this issue.