The main problem using Dropbox is missing path for libraries and added files. It happens because on different computers paths to Dropbox folders on hard drive are different - let say using Windows and Mac. Also paths for publishing sets. So every time opening file, that was in use on another computer, you need to check and possibly re-link libraries and also check right path set in publisher before issuing drawings.
Another small problem - that two people on different computer can open the same file. But in that case you will get notification while opening file, that file is opened on another computer. Just ArchiCAD creates small text file when you open a PLN file (and deletes when you are closing file), that reads another computer before opening the same file. But sometimes, if system crashed, this notification file can stay - and you can get notification, that file is in use, when actually it isn’t.
But apart of that - all fine. I was working almost a year like that, before we decided to switch on BIM cloud.