I presume you bought a used Crosscheck or else you could have the dealer tune it. Start by cleaning the drivetrain with a degreaser and then lubing the chain. If the shifting problem is at the highest or lowest gear, then the stops may need adjusting; two small screws on each of the deraileurs limit the max. travel in and out. The RD hanger may be bent a bit, so look at that; ditto with the front; sometimes things are just a bit out of alignment on frame for the FD: “twisting” the mounting clamp a little can solve some noises.
The bar-end shifters are cheap enough to replace if they feel sloppy; and you can tighten them up pretty easy, too. They also are capable of friction or index shifting modes. Try moving the rear one to friction shift instead of index shifting or vice versa; turning the ‘knob’ on the side of the shifter switches things from one to the other. Friction shifting may work better as you can move the shift lever just a tad to fine tune the shift, whereas index shifting uses ‘clicks’ to find discrete positions.