I have this 6500 mile, ten year old Mongoose hybrid with twist grip shift whose RD is no longer shifting correctly. After 4000 miles or so it would only shift smoothly one way, larger cog to a smaller. I went thru the adjustment routine in ParkTools and got it to shift smoothly the other way, smaller cog to larger. But never smoothly in both directions. Right now it takes two 'clicks' on the index to shift to a smaller cog, but the normal one click to a larger. Cable and twist grip work fine. It does not look bent. A replacement RD would be about $25; but I would like to fix it, (Shimano C105 7 speed freewheel Megarange, low normal).

How is the chain? Pretty clean and adjusted properly?
Also the shift cable? It might not have any kinks in it, but is there any slack down near the derailleur or up in the grip-shift unit?
Try lubing & cleaning the chain, and maybe put a drop of Tri-flow or other light oil on all eight of your derailleur pivot points. In fact, shift it to the largest cog, lube those pivot points, then to the smallest cog and lube them all again. Then wipe off the excess and see how she does.

At 10 years old it is possible that friction is building up somewhere, either in the derailleur or the cables. I would suggest that in addition the lubing the derailleur, as suggested above, you lube or preferably replace the cable and housing. Pay special attention to the short loop of housing going into the derailleur, it often picks up road gunk and water. If you decide to change them out, die-drawn stainless wires and lined cable give good performance and last well. Make sure that they housing runs are the correct length and that the housing ends are cut or filed flat and the correct ferrules are installed.

The most likely cause is a sticky cable, especially considering the age. The first place cables bind is usually in the rear loop because of faster wear on the inside of the sharp curve.

There's an easy test, which will confirm rear loop friction, hang the bike so you can pedal and shift by pulling the bare wire away from the downtube. If it shifts smoothly, the rear loop is OK, but if you find the RD doesn't move freely, or hangs up when you slowly ease off the tension. You can sometimes get an even better feel by removing the wheel and feeling/watching for smootheness or binding as you work the RD through the range.

Given the age, if the cables are sticly, odds favor replacement over trying to save them with a clean and lube, though you could give that a shot.

If you end up replacing the cable, you might want to check the innards of the Grip Shift mechanism. All it consists of is a steel spring. Get some silicone grease (the SRAM equivalent is called "Jonnisnot") and lube the spring, then install the cable and re-assemble. Also, if your shifter has an adjusting barrel, unscrew it and lube the threads, then screw it back on.

Shift into a gear combination that makes the derailleur arm point downward. Then prop your bike up against something and look at the derailleur from the back. If it looks like the derailleur arm is pointing toward the tire - that's it.

Whenever i encounter a rear shifting issue that doesn't respond to normal tuneing, the first thing that I do is to check the derailleur hanger alignment. Most of the time, that's the source of the problem.

Derailluer pivots can wear out and cause the problems your describing.

Thanks for your replies. I've tried most of the solutions suggested, except changing the cable housing, which I will do. As Diesel Dan says, it may simply be worn out.

Well not so fast! I checked again, and as Retro Grouch cautioned, the DR arm IS pointing toward the tire, ie hanger alignment problem. Anyone ever try placing a shim so the DR would correct to vertical? Maybe a clipped off piece of ziptie or something. Or is it time for a new DR?

Just clamp a big adjustable wrench over the derailleur where it attaches to the frame and gently bend it straight. With a 7-speed I can get it close enough to index by eyeball. On a 9-speed I have to use a gauge (bike shops have them, it's about a $15.00 or $20.00 job.)

Don't be tempted to unbolt the derailleur and try to straighten the hanger. You might ovalize the derailleur mounting hole.

You can't shim hangers. You gently bend them straight.

Steel hangers are very tolerant of bending (cold setting for folks who speak tech) but aluminum hangers much less so. So it's best to straighten the hanger in a single shot, rather than working it back and forth drying to dial it in. In a pinch you can stick an allen wrench into the upper pivot bolt and use that as a bending bar. If you have a replaceable hanger, and the bend is sever, consider shelling out for a replacement.

One trick is to thread a front wheel into the hanger to bend it back. You can sort of eyeball the alignment. I did that with a 20" wheel on a recumbent, as the alignment gauge wouldn't work on the smaller wheel.