When I bought my serger, I made a point of getting one that has coverstitch capabilities. Ready-to-wear knits have lovely, flat hem stitching that stretches just the right amount and never draws up or ripples, in contrast to everything I've ever tried on a "regular" sewing machine. Here's how pretty the two-needle hem turns out on cotton interlock.
However, my serger skips stitches when coverstitching over seams. That means on two of these tee-shirts, there are skipped hem stitches at each side seam. I wouldn't normally get too excited--it's only one or two stitches. But coverstitch is a lot like chain stitch--if you give a loose thread a tug, you can pull the whole hem out in one fell swoop. I tried everything I could think of to solve this--sewing very slowly, tension adjustments, shims--but there was always at least one skipped stitch, and therefore, one place where the hem could be snagged and pulled out.
I searched the Internet for a long time before I found this handy tutorial on the Gigi Sews blog: Coverstitching over serged seams. She clips the seam at the hemline, then folds the seam edges in opposite directions. This gives you a much flatter "lump" to sew over. She claims great success with it, and I plan to try it soon.
I also went through my closet looking at ready-to-wear knit hems, and got a surprise: None of the coverstitched hems were stitched over a seam. The garment pieces were hemmed first, then assembled.
To summarize, there are two ways to handle coverstitching over hems: avoid it, by hemming before assembling, or clip the seam and fold the overlocked edges in opposite directions before hemming.
There are some fabrics where coverstitching just may not be an option. The paler yellow tee-shirt, above right, is a super-stretchy performance fabric (along the lines of Powerdry, but a different brand), and it was just about impossible to hem--you can see I gave up and finished the cuffs and bottom edge with stretch lace applied on my regular sewing machine.