Most interesting answer from you Liz, because I respect the advice you have
given over the years. We certainly entered Tanzania on a UK and Canadian
passport without any Tanzanian documents, but with a Kenya visitor's visa.
You have to ask, or they will sell you anything! It was only after a long
talk in the Tanzanian consulate in Mombasa that they admitted that a
Tanzanian visa (which I needed because I was a Kenyan resident) was good for
multiple entries over a three month period. Until then I had dutifully
bought a new one for each entry.
I would suggest to prospective travellers that you ask several times before
you pay out for a visa. And if you plan on buying one when you land, make
sure you have the correct amount because nobody will be able to give you
change!!