Some thoughts.
Skipping between gears - could be bent, worn or misaligned rear gear changer/hanger, possibly too short an arm rear changer with a mega range block, worn out indexed gear changers...or probably as you surmise a lack of cable adjusters for fine tuning.
Chain jumping whilst remaining in the same gear - could be worn chain, block, chainrings, or low chain tension from too long chain, too little chain wrap round block...
I hope this helps.