With an allosteric inhibitor (AI), you mentioned that either Vmax or Km can be changed. Then can I say that the apparent Km will be the average of the weakened enzyme molecules and those remaining uninhibited, thus the apparent Km will increase?
From its remote binding site, an AI could affect the shape of the substrate binding site, thus changing the binding affinity andthe apparent Km. In a mixture of inhibited and non-inhibited enzyme molecules, I would expect the Vo vs. S curve to be complex (biphasic?) and not yield an "average" Km.

Is it safe to say that the only difference between non-competitive inhibitors and allosteric inhibitors is that allosteric inhibitors bind to a remote site in the enzyme whereas nci bind close to the active site?
A consequence of the fact that allosteric inhibitors biond to a remote site is that they must distort the protein so as to 'telegraph" their presence to the active site. In contrast, a non-competitive inhibitor need not do so: it could bind to the active site pocket, but not to the part of the active s ite that binds to the substrate.