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I too have been having related problems since shortly after upgrading to 365 / 2013 (we're now on 2016).
EDIT: I should also mention that this happens across multiple different machines running multiple different builds of 2013/2016 with many different workbooks. It is not confined to one machine, Excel version, or workbook. It is a general problem that has existed since at least 2013 (and possibly before, although we skipped the previous version so can't comment).
Sometimes, when typing in a cell on Workbook A, when I press enter nothing appears to happen. If I then switch to a different workbook (let's call it Workbook B) that I had open, the value I was typing into the cell on Workbook A is put into a cell on Workbook B instead.
Also I find that Excel is regularly failing to redraw things - e.g. clicking on a cell to activate it *seems* to have no effect, or trying to set a cell's Style seems to have no effect UNTIL I switch to another open workbook and back again, whereupon the changes I made become visible.
Switching to a different application and back does not solve the issue - only switching to another workbook and back again seems to redraw Excel's window.
Info I can provide:
It *seems* to get worse/more frequent if I have had a workbook that contains external data queries (e.g. queries from SQL Server) open, however I don't think that's the root cause (it happens on workbooks without any queries or VBA in them). Also I can't be sure on that, I've just noticed that a certain workbook that I have a load of queries in regularly causes more frequent redraw failures. The bug can occur even without any query workbooks open though, so it's not exclusive to that - it just seems to make it worse.
It is sometimes triggered by setting a cell's Style (I have a variety of custom Styles set up that I use regularly). Everything can be working fine, then sometimes (not always) when I set a cell's style (even in a brand new VBA-less and query-less unsaved workbook), nothing appears to happen until I switch to another workbook and back, whereupon I see Excel redraw the cell with the new style and adjust the row height to match the new font size.
It's worth noting that there are plenty of threads around that point to ActiveWorkbook being incorrectly reported in VBA, possibly due to the Activate method of Workbook not working properly - one guy discovered that his call to Activate was often followed by an internal call to Activate on another workbook, hence ActiveWorkbook returned the wrong value. Although I appreciate that most of this thread is from users who are NOT using VBA, I mention this because it seems to be a VERY similar and possible related issue - the wrong workbook being activated internally somehow.
I also think that waiting 3 years (and counting) for a bugfix for something so ridiculously basic as the UI behaving how you expect it to behave is dreadful behaviour from a software developer. Microsoft should be ashamed of themselves. I appreciate that Excel is a large and complicated application, but when you've got this many people unable to work for the same reason, you boot it up the priority list. We can manage without new features - fix the bugs first!