Thanks for the bug reports @rlivett. We are in the midst of fixing the bugs you have mentioned.
The reason you can’t close the desktop app, is most likely because one of your cards is in edit mode (if this isn’t the case please let us know). We purposefully prevent you from closing the app when you are editing something, but the app isn’t displaying the correct popup to give you the option to quit. This will be fixed in the 1.8.2.
The Today / Thoughts ‘card counts’ are also being inconsistent at the moment (will be fixed in 1.8.2), but your cards should be saving and updating ok! Again please let us know if this isn’t the case.
In the meantime while the desktop apps are still in Early Access, I recommend using either the web app or desktop app (not both at the same time) on the same device.