You can check the input part of it all on the client sure, but a lot of that info could be recorded as well
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Yes there's stuff that can be more or less impossible to detect at demos, at which point more data could be included in the actual demo, to improve the effectiveness.
My point is that, yes you can do cheat related stuff that's more or less undetectable at demos. But if you're capable of doing that, you're also more than likely capable of working around any clientside countermeasures, hence they're not safe to rely on. A large archive of every demo from every record a player has set is in my opinion a better solution (gives more to work with\go on). While of course some other things could be added without notice (both client and serverside), causing potential "busts".