The main problem--if you think of it as a "problem"--with monotheism that I would consider to be "logistical" is the lack of the one great convenience that comes with the usual squabbling pantheons of polytheistic religions: You can't play one deity off against another. Monotheism requires us to really and truly worship our one god (or goddess, if that's your preference). And so--as the slow development of the idea throughout Hebrew scripture attests--monotheists eventually have to make sure that deity is worth worshiping, in all possible ways.
There's also the problem (e.g., among Christians, Jews, and Muslims) of deciding who worships the same deity and who worships a different one. But that's been considered by others:
‘People killing one another just because their gods have squabbled—’
‘Oh, they’ve got the same god, sir. Apparently it’s over a word in their holy book, sir. The Elharibians say it translates as “god” and the Smalies say it’s “man”.’
‘How can you mix them up?’
‘Well, there’s only one tiny dot difference in the script, you see. And some people reckon it’s only a bit of fly dirt in any case.’
‘Centuries of war because a fly crapped in the wrong place?’
‘It could have been worse,’ said Carrot. ‘If it had been slightly to the left the word would have been “liquorice”.’
-- Terry Pratchett, "Jingo"