While there are many benefits in using MusicBrainz as the primary source of your metadata tags, there are a couple of issues which need to be considered.
Firstly, if you amend the data in MusicBrainz, it may be that your changes are quarantined for 6 days before being effected (new data is normally applied immediately). Unless you change the tags on your music files manually (which rather spoils the point of using MusicBrainz and Picard), you need to remember to re-tag the files in Picard at a later date.
Fortunately, there is a fairly easy way of dealing with this. Set up a (private) collection in MusicBrainz called (say) “My edited releases” and add your edited release to it. Then, from time to time, you can check your collection for releases which no longer have open edits: re-tag them and remove them from the collection. If you have edited a work rather than a release, then you will need to set up a work collection rather than a release colllection (and similarly for other types of entity).
The other issue is that other editors may amend releases that you have tagged. Generally, this is to be welcomed as more / better data is added. Occasionally, though, edits may be in error. Either way, you may wish to know about it, either so that you can re-tag with the new data, or query/down-vote/amend the edit.
Again, the solution is to make a collection. Picard allows you (in the context menu) to add releases to a collection, so just set up a collection called, say, “My albums” and subscribe to it. Then, when changes are made, you will be notified about them. It is also possible to set up collections of all the works you have and be notified about changes there too. However, at the moment, this can result in a lot of notifications which are simply people adding new recordings of those works - ideally these should be screened out as they will not affect your own tags in any way. If you still wish to add works you have recordings of to a collection, I have written a small plugin which adds this capability to the context menu in Picard.