I'm more of an editor (and a student one at that) so please take this with a grain of salt.
I think the coverage method can be a good idea, although be careful not to overdo it. If you are working on smaller movies with actors who aren't really being paid sufficiently for their time try not to take the same scene 20 times because the actors performance will become mechanical.
Try to make each different angle work... I loved the movie 'The Shining' for this. The carpet, the tapestries on the walls and how they balance Jack Nicholson inside the frame... More than continuity I'd look be striving for purpose and balance.
Think about getting reaction shots. Closeups of faces, emotions, etc. These can be great transitional elements. Production value goes a long way, but in the end it's the story that makes or breaks a film of any budget.