The Solex 4-barrel carb really isn't that bad, though its reputation is. Most of the problems with those are from over-tightening the air horn (upper half) or just a plain lack of knowledge about how it works. For instance, if you "poke" the secondaries open with the throttle closed, a plastic piece breaks on the secondary shaft inside the air horn. Not good...
The first rule is, "If you don't know what you're doing. don't"
The second rule...see rule one.
But seriously, those carbs can have all sorts of weird problems from the needle and seat coming loose, to binding secondary needles and flaps. Find some one that has been through the learning curve on those.