Is there any reason something weird would happen after downloading a paused save?
I'm not familiar with pausing so I have no idea what fiddling you can and can't do.
It seems that you can do quite a bit without affecting the game...
a) you can swap squares worked by a citizen in a City (which is already allowed since it is a reversible action) without having the squares update (although this fact could be annoying, we really should be using a test saved game for this activity anyway, as long as our test saved game stays up-to-date)
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b) you can give orders for a unit to move without it moving, which is probably the primary benefit
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c) you can enact a trade (presumably accidentally accepting it) and the trade won't actually resolve itself until you unpause the game. The behaviour here is weird--to avoid you trying to barter the same tech twice with the same AI or to barter with other AIs to avoid things like We Fear You Are Becoming Too Advanced limits, the game prevents you from opening any other trading screens until you have unpaused the game... which, in a good sense, if nice, since this functionality means that you can't abuse the Pause mechanism for getting around the game's trading rules
While the game is paused, you can still ask an AI what they would like to trade, but it appears that you can only speak with one AI per paused session, even if you don't make a trade. In fact, all that you need to do is click on a leader's name and even if you don't open the trading window, you won't be able to access another AI's menu of options until the game is unpaused or else loaded again while staying paused the whole time.
Thus, having the game paused when we first learn Alphabet could be more of a hindrance than it would be a help.
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d) you can delete a unit without it actually being deleted (even if you confirm that you want to delete the unit) until you unpause the game... in fact, any unit action (i.e. a hotkey being pressed, such as "e" for Explore) will also not register
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e) you can try to click on the tech bar to change your tech but that click won't register until you unpause the game. You can still view the F6 Technology Advisor, though, so that fact isn't really a hindrance
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f) you can even accidentally click on the "End Turn" round circle (either green or red) and not have the turn end until you unpause the game. Of course, this fact can lead to an unexpected ordering of events... if you tried to talk to multiple leaders and also clicked on the End Turn icon, after unpausing, the turn would end and THEN you'd get to talk with the leaders--on the following turn
I like to leave a unit with movement points available to it when uploading a saved game to avoid someone accidentally pressing the Enter key or Spacebar key and inadvertantly advancing the turn. Since this team is terrible at actually following this process, then Pausing could also work... but we're just as likely to forget to pause the game.
I think that the best policy is going to be:
a) Let's upload the saved game unpaused. As ZPV seems to imply, we don't need to go gung-ho crazy here on instituting over-cautious behaviours
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b) Maintain the highly-desired suggestion of leaving a unit with movement points remaining when you upload the saved game (such as unfortifying a unit in a City that doesn't need that unit for Military Police in order for the City to remain happy)... normally unfortifying your capital's Warrior is workable, but if we're at the Happiness cap there, then it would be preferable to leave a different unit with movement points remaining
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c) Do your own pausing. Try to be just as careful as normal and don't take the cavalier attitude that playing with a paused game is a free pass--but at the same time, feel free to pause the game to add an extra layer of safety before you look around at the saved game