Isn't it a problem from authenticity standpoint? I mean you cannot sign a check by putting into the printer and have your signature printed on it, even if you made it unique. Wouldn't it be better for future authenticity checks if the signature is made with a pen of some sort?
Actually, yes you can. Facsimile signatures are extremely commonplace in the corporate world. Too many cheques being written to waste a senior exec's time manually signing. Manual signatures, these days, are really only done by small businesses that can't justify the expense of the cheque printing/signing printers and related software. Even cheques are going the way of the Dodo bird as more payments are done electronically.
Back to the original question, though.... Historically it was considered bad form to sign on the actual printed area. The print is sacred and should stand on its own, unadulterated by a signature. Photographers today who don't have the sense of history or haven't learned from an 'older' pro will have a greater tendency to sign in the printed area. This is becoming more true with newer media like canvas where the image is being treated more as, and considered as more like, a painting than a photograph. Borderless printing methods also make it difficult to avoid signing inside the printed area unless the signature is on the reverse. Farming out printing and framing/presentation also makes it difficult to have the print signed, which is a good reason only to farm out printing (if you have to farm out anything at all) and have the print delivered back to you for presentation before it goes to the customer. If signing on the reverse, care needs to be taken where the signature is placed so that it doesn't affect the front of the print from pressure of the pen/pencil.
As far as what is used to sign, if you're going to use conservation methods and materials then you want to do the same with the signature or any other information included on the print. Pencil is a classic. There are numerous types of pens available that are labeled as acid free.
Editioning is what it is. And there are arguments on both sides of the fence as to the worthiness of editioning. But there's no reason not to sign an open edition print. What you may consider doing is providing a certificate of authenticity. Terry's posted an example. I do something similar. What I also do (and, again, there are arguments on both sides) is create a unique alphanumeric identifier for each print. That identifier is written on the print and is put on the COA. I tell buyers that the two should be kept together or if the COA is to be stored separately, it should be kept in a place where it won't get lost, damaged or forgotten. Personally, I sign on a non-visible area of the print. Typically that's the unprinted border or for canvas on a portion of the canvas that will be wrapped around a stretcher. With matted/framed prints, I also sign on the mat.
Re: manual or digital signatures on prints, while cheques can have facsimile signatures, doing so on a print would lend credence to the audience that feels photography isn't as legitimate an art form as other visual arts. It lends credence to the idea that the photographic print is a 'reproduction' and not an original. Quality of handwriting really shouldn't matter. Plenty of artists have/had bad handwriting. Sign the prints manually. Manual signing also lends a more personal touch and removes the idea that it's simply a mass produced piece that could be bought at Wallyworld. A signature in pencil will always be evident as manual but with some pens, it can look like a reproduction.