Running the SQL Server Performance Dashboard Reports (nice name) gives lots of suggestions for missing indexes in my DB. Should I implement all of these uncritically? Or should I "sort" them somehow and decide which ones I should implement?
Should you blindly implement every "Missing Index" suggestion the report makes? No.
Should you look at its suggestions, evaluate which ones make sense (would eliminate frequent table scans but not bog down the server with overly-frequent index updates) and implement those? Sure (and if you're having performance issues, absolutely!).
Like all suggestions from software tools you should consider what it's telling you, but never blindly substitute its judgment for your own.
No sir you should not. Instead use the recommendations as the starting point for your analyses.
Consider also that the performance dashboard reports will be presenting you with recommendations for queries that are currently in the plan cache only. The missing index DMV's on the other hand will contain a complete history of recommendations since your last SQL Server Service restart.
To learn more take a look at this excellent tutorial video over on SQLServerPedia: Find Missing Indexes
You will also find T-SQL scripts you can use in order to query the missing index DMV's here.