My uke is a good quality one. It is a Mitchell MU-70 Concert. It came with GHS strings. I have it tuned correctly. It only does it on some chords. But I don't think it is my fault, because I will put my fingers perfectly (going really slow) and it will still buzz sometimes. When I strum without holding the strings it does not buzz. I am brand new to ukulele. Hopefully it is just the strings.
I loved the MU-70, but I had to take it back for the same reason. That plus the saddle was not set up right and there were tuning issues. But it is a pretty instrument for the price and the spruce top projects quite well. The quality control on these vary quite a lot.
OK, troubleshooting here: The reason it does buzz on some chords and not others is that certain strings at certain frets are buzzing and others are not. Play a chord on which it buzzes and then play each string that is being held down individually. Play another chord that buzzes and see if it is the same string. If it is, is is a set up issue that may or may not be able to be fixed.
If it is not, it could be a frequency thing where, at certain frequencies, it is making something else buzz. Loose piece of wood, stray splinter or something. On my Cordoba, a loose tuning peg was buzzing like this, but only when I played certain frequencies. Hope this is of some help.
I never got another MU-70 and I know some people will diss them, but I loved the tone of mine, for what little time I had it. I have a friend who makes mandolins and he did some work for me on my Cordoba and I thought about getting the MU-70 and having him work on it, but I never did. Best wishes!
Mike