Should my skin graft on my nose turn black after mohs surgery?

Sometimes skin grafts are the very best option...depending on the size and location of the hole.  However, skin grafts are often not our first choice for many reasons (i.e. mismatch with surrounding skin, slower healing, fragile nature of grafts, and a needed "donor site").
Skin grafts are almost always ugly early on, especially the first 2-3 weeks.  However, a black skin graft can be a bad sign.  #1 Sometimes grafts look black simply because there is a layer of dried blood on the surface.  Very careful cleaning of the dried blood (by your doctor/nurse) may reveal a healthy graft underneath.  #2 Sometimes grafts are a little dark and dusky looking the first few days while awaiting ingrowth of a better blood supply.  #3 But, if the graft is completely black after several days, this usually indicates that some of the skin graft has died.  Sometimes the loss is limited to the upper layers of the skin ("superficial epidermolysis") and sometimes it involves the entire thickness of the graft ("full thickness necrosis").  
In most circumstances, the best option is to be patient because the wound will often fill in from underneath and from the sides.  Even if some of the skin graft has died, it can act as a "biologic" dressing while the wound heals.  Less often, it may be advised by your doctor to removed the graft and either allow the wound to heal or proceed with an alternate procedure.  Healing may take 6 weeks or more.  After 6-7 weeks a logical decision can usually be made as to whether a revision procedure should be performed.
The loss of a skin graft is an unfortunate reality that is NOT necessarily due to surgeon error.  Skin grafts are delicate...skin that has been completely separated and then reattached to the human body.  The skin graft no longer has blood vessels directly supplying the oxygen and nutrients needed to survive.  Instead, the grafts undergo a vital 3-step process allowing survival and eventual reestablishment of a reliable blood supply (the 3 stages are referred to as "diffusion", "inosculation", and finally "revascularization").  Unfortunately, skin graft healing can be disrupted when bleeding, infection, or "sheer" forces do not allow oxygen and nutrients to sustain the graft.  Also, the underlying body area may have a poor blood supply due to the location (i.e. lower legs and feet) or due to other treatments (i.e. radiation treatments, scar tissue or steroids).