I have had an H001 for several years; it is my squirrel rifle and, like most .22's, is very accurate with ammo it likes.
They are designed differently from other lever guns in that what appears to be the receiver is really a carrier for an internal receiver. The serial number, which must be on the receiver, will be found on the lower portion of the actual receiver in the wrist of the stock (where the lever rests with the action closed). When I first got it, now and then the extractor would slip off of a cartridge rim. I inspected it and found that the design of the receiver/carrier resulted in just a little excess play that would allow the bolt to move enough to the right so that the extractor would slip off. I placed a very thin shim inside the carrier on the right side of the bolt to keep the bolt to the left. That stopped the problem, at least with .22 LR ammo. Aguila Super Kolibri will still do it now and then, but they will also do it in other guns.
I wanted to modify the front sight by installing a tiny white bead on the face of the sight. I wrote Henry and asked about buying an extra one for this purpose and they sent one along for free. (I have used the modified sight to good effect many times, since the white bead stands out so much better than the black blade.) I know I could send the rifle back to them and have the issue with the extractor fixed properly, but it is working fine and I don't want to be bothered with the shipping, etc.
From all accounts, their customer service is second to none. I don't see how they can build such a high quality product for the price. I am thinking about getting one of their .22 pump action rifles.