You should check the bridge very carefully, any loose screws that rattle? Is the string holder piece (or whatever it is called) okay and the saddle too? Is the string height reasonably similar to the other strings? Are the frets okay at the first frets? Are the frets even and smooth, are there any dings that damp the fretted note?
You should also check that the neck relief is adequate.
The string sustain and tone
are different between open and fretted notes of course so they never sound exactly similar.
And last but not least, you should check the bass played through an amp in a band situation, does this really affect the tone or the playability? If it does, you should take care of it and see where the problem is. But I've also noticed from personal experience that one can be a bit too neurotic with a new instrument and things that really don't matter in real life situations seem to grow to intolerable imperfections