New chain with old freewheel will do this. The old freewheel's teeth may have been slightly reshaped by a stretched old chain. This happens most on the gears used most - which could explain why it's only a few of the gears playing up.

If this is the case then a new freewheel will fix it.

Indicative diagnosis would be to run the old chain if you still have it. If it's quiet with the old chain then it's unlikely to be the BB.

You can only run a new chain on an old freewheel if you change the chain before the old one stretches beyond a certain point.