Problems.
--Anchor points for shoulder straps
Solvable with some smart engineering. Particularly with the new seat designs with rigid backs that 'recline' by sliding the seat bottom forward.
--Getting pax to put shoulder straps on when they moan at lap belts
Make the shoulder strap independent from the lap section so it doesn't have to be worn for other then take-offs and landings. That will obviate the need for pre-tensioners. These are used in autos where the lap/shoulder belts are slack (spring-loaded winders in most cases) and need to be pulled into place in the event of an accident. A shoulder belt only needs to be snug for a few minutes so its not too much to expect them to be worn correctly. Passengers don't like it? Take the bus cross country the next trip. No belts required.
--Getting the beancounters to accept the extra weight/cost of shoulder straps and tensioners.
Tough. And until they start charging overweight passengers, I think they can live with a few extra pounds per.
--Issues with escape when pax are secured by lap and shoulder straps.
Same as for lap only belts. A one handle release should be easy to design.