for multiple occurences of street names.. how do you propose to differentiate? how do other nav apps handle that? does OSM contain other identifying properties?
monav sorts the selection list by 'size', so the biggest street comes first. and if your first try is not the right one you can go back and choose the other. Is that so hard? maybe I just don't get your problem..
The missing street names on the map is a known issue, hopefully soon resolved.
so, summarizing: no problems whatsoever with address lookup..