v3 introduced using ! to negate character classes, in addition to ^. If any of your patterns include a character class that starts with an exclamation mark (ie, [!...]), you'll need to update the pattern to escape or move the exclamation mark. Note that, like the caret (^), it only negates the character class if it is the first character in the character class.
The change from v1 to v2 was fairly minor: the return type of the Open method on the OS interface was changed from *os.File to File, a new interface exported by doublestar. The new File interface only defines the functionality doublestar actually needs (io.Closer and Readdir), making it easier to use doublestar with go-billy, afero, or something similar. If you were using this functionality, updating should be as easy as updating Open's return type, since os.File already implements doublestar.File.
If you weren't using this functionality, updating should be as easy as changing your dependencies to point to v2.