Depends...
With PanF+, the notorious film when it comes to latent image (in)stability, the advice is to process ASAP, as in within a few days or so. Don't let it sit for weeks. A film like Kodak TMAX100 I think you can pretty safely store away exposed for a month or two and not notice the difference unless you do critical analysis on it. With color film, there's generally slightly less slack, but even that is mostly designed to work well if you take it on a really long holiday and only develop it after weeks. I never really encountered problems even with the occasional roll that was stuck in a camera somewhere for a couple of months.
The image just fades; overall loss of density, the shadows going first. Color film will shift.
I guess we all know those examples of the roll of film forgotten inside a camera and developed after 10/20/30 years exhibiting serious problems. But apart from this, I never experienced latent image stability as a problem.