I have a 12 x 14 shed with 16 inch on center floor joists resting on sleepers on the two ends and in the center to support the down. However some of the 2x6 floor joists on the end are shy of being flush with the butt joint fronts (maybe 1/8 to 1/4 of inch due to end of one being skinnier) when resting on the sleepers. Can I shim under the floor joists to lift them up and if so what is the best method for this?
With shed framing, 1/8" is rarely a concern. 1/4" is slightly more so, but still not much in this case. You could leave the joists resting down on the sleepers, install your floor sheathing, and build your walls with no ill effects. It's a very minor cosmetic issue if anything.
If you like, shim the rim up flush with the top of the joists. Just be sure that you aren't introducing humps in your floor, which would be a much more significant issue. Use a long level or other straightedge to check that out.
Correction: I see now that it's the rim that's low. Just float it. All the load of the walls and roof will be carried by the common joists. It's not a problem at all.