I own a 6.5" blue finish 4410 Taurus with a 2 1/2" chamber, and this is what I have found...
With .45 Colt ammunition of the standard load variety, it functions very well, and have never had a problem. Not all bullet styles seem to shoot alike- it did not like the few rounds of Winchester Silvertips that I ran through it- they shot 8" low at 15 yards. The regular 250-255 grain Space Coast bullets that I load for plinking shoot to point of impact and group as well as I can shoot it.
As for .410 shells- they are a horse of a different color altogether!
The problem is, that not all .410 loads act alike when shot in a chamber that is slightly larger than what a .410 chamber should be (.45 Colt).
Stay away from Rio and Fiocchi .410's to shoot in the Judge- the head of the shell seems to expand much more than other brands and will either require the extractor to be pounded a bit to get them out.
Winchester and Federal ammunition seem to be the easiest to extract and shoot.
Also, don't think that this little gun is going to shoot and pattern like a regular .410 shotgun, because it won't. The rifling and shortness of the barrel cause the shot to spread very, very quickly. To combat this for small vermin, stick with #8 or #9 shot to keep the pattern somewhat denser than that of the larger shot sizes.
Another alternative is what many people have been doing- putting an extension on the barrel with a straight rifled choke tube from a Thompson Center Contender or Encore .410 on it. It does improve the pattern significantly I am told, and have talked with a gunsmith that does this.
All I can say is that it is great fun as a "rat gun" off of the tractor loaded with AA #9's while bush hogging.
Let me add that it shoots identical to my Contender when the choke tube is out of it.