The first idea that jumps out in my mind is using this with other coworkers. It would save a lot of time if 2 or 3 people were working on a Power Point presentation or other documents. We collaborate sometimes, but often times, as a new teacher especially, I'm making a lot from scratch or at the very least tweaking others' ideas. For example, I just worked on and uploaded a Power Point about Las Posadas (Mexican Christmas). Because this information won't change (for a while...), it would be beneficial for all Spanish teachers to have a copy of the presentation online. We could agree to show it for Spanish 1 classes. The Spanish teachers like to switch the level they teach each year; for example, I should hypothetically get Spanish 2 next year. If we created notes about Spanish holidays for each year (or other topics) then I could just go to Google docs and retrieve. This would save myself time from creating something brand new, and it would save the veteran teachers time from having to answer my emails : )
I could see Google docs being beneficial with writing assignments for English. Often times students have problems converting a document they were working on in class to be compatible with the programs they have at home. This would be a huge benefit! It would obviously be helpful for group projects, too. This way students don't have to worry about bringing in flash drives or who saves the work to whose file because they would all be sharing the same file online.
Personally, it would save me time also from saving information to a flash drive and then uploading it onto my work computer or emailing myself documents I've created at home.
Problems would involve setting up the students' email accounts and teaching them clearly enough so that they understand exactly how it works and are able to use Google docs at home by themselves. Other potential problems might be students trying to copy each others' work online , which would be more difficult to monitor (of course, if the final products are the same it will be obvious what happened).
For now, I can see more advantages than disadvantages to using Google docs. Perhaps once I try it out more (both for me and with students) the disadvantages will be clearer.