I have been in my new Mobile home now for 5 months.Nails are starting to pop up slightly under the linoleum floor. Is this likely to get worse over time?
It will certainly worsen. The nails are probably coming up because the subfloor was not glued to the framing. Not only will more nails work up, but the vinyl will very quickly wear through in those spots.
I agree that this is certainly a warranty issue. If you're not able to get satisfaction from that, you'll need to re-fasten the subfloor and reinstall flooring. I'd probably run suitable screws at 12" intervals on all joists, then fill the dimples and overlay new vinyl. An embossing leveler may be necessary to flatten the texture of the current vinyl.
It has a possibility of getting worse or the popping could be done. It's hard to say one way or the other.
Definitely get the foundation checked-out & call for warranty service. A framing member may have been damaged/defective or there may be a temporary support that was left in place instead of removed or the foundation is contacting the wrong area or not contacting enough areas.