Yes, some aspects of Moshi Monsters Rewritten will have some progress bugs.

This includes the missions and the underground disco. The missions will not save your progress since it's still a major work in progress but will be fixed in the future. The underground disco, for now, isn't a major issue and you can continue to unlock songs over and over again just what you have unlocked will not save.

With that said, we do have some visual bugs in relation to some of the games. Games such as The Great Beanstalk will grant you the XP just your level bar will not rise until exit the game via your room or refreshing the application. 

Colorama at the port will save your colors temporarily and then revert back to the colors you selected via signing up. For more information about the Colorama see: https://moshirewritten.com/help/tutorials/how-can-i-change-the-colors-of-my-monster

Room ratings will seem to be loading foreeeeeever, but on the contrary, it does save!

   Update as of August 2021: Room Rating Bug has been fixed!

Some gifts that you receive may return to being unopened, the quick fix is to reopen it - Who doesn't love a free gift though!