New Input Source Options
Open System Preferences, click the International icon, take a look at the Input Menu tab. The age-old "Font and Keyboard" synchronization options have been replaced with something far more useful (and understandable!). Specifically, the "Allow a different input source for each document" option means that Spell Catcher's input method can be active only in those applications (and more precisely, in those documents within an application) that you need it to be active in. Give it a try - open TextEdit, make two new untitled documents. Activate Spell Catcher's input method in one of them. Choose a keyboard layout in another. Switch between documents, watch the input menu.
The first radio button (Use one input source) will give you behavior similar to what you're probably used to with previous versions of Mac OS X (not exactly, but similar). The second (Allow a different input source) gives you more flexibility if you're someone that uses different keyboard layouts and/or input methods in your normal workflow. Try them both, see what works for you best.
Important Things to Know
If you think that Spell Catcher's input method keeps "turning itself off" - well - it's not. Actually, it can't. Only the OS itself can properly deactivate an input method. There's no way for an input method to activate or deactivate itself (none that I'd consider using, at least - and even if there was, it's not something an input method should be doing, anyway!).
First thing to check if you believe this is happening, but don't want it to: Choose the "One input source in all documents" option (see above).
Realize that OS X enforces the fact that no input method can be active when in an authorization dialog or some other sort of secure (password, bullets) text entry field. It's perfectly normal to see the input source change to a keyboard whenever you have to authorize.