I do the same, but it is a hassle. I constantly get warnings in KeePass that the database file has changed and have to click 'Yes' so it merges the changes. It's always worked so far, but I guess if I click the wrong button I will loose an entry.

Sometimes I get conflict files in the Dropbox folder. Not often, but a few times over the last year.

On iOS I have to open Dropbox and re-export the database file to see new entries. If I ever want to add or change an entry on mobile I have to manually export the file back into Dropbox. If the database in the app wasn't up-to-date, that will loose any entries added on desktop.

The KeeFox extension for Firefox works but is unreliable, especially on Linux.