I got a watermelon from a neighbor that had tiny white seeds--I thought it might be a growing problem rather than a variety. I didn't grow it and I don't know where she got it--does anyone think there might be problems with including it in my landrace?
Well i guess it depends on if the seeds were flat and undeveloped or if plump and fully developed.
True "seedless" watermelons still have seeds, they just won't grow because of the chromosome mismatch of a tetraploid crossed with a diploid.
But otherwise, if they grow, then they should be fine. They may not be adapted to your climate necessarily but i don't see any problems other than that.
I suspect the seeds your neighbor gave you might be flat and unviable, but without more information it's hard to know for sure.