There is no fully automatic way to clean up after such inventive "typists."
One way would be to place or paste the text in InDesign, then use Find/Replace to identify and delete all the instances of space-space, space-tab, etc.
Another thing that comes to mind is this: In Word, a little-known feature is the ability to select text vertically. Hold down Alt while click-dragging to select one of those faked-up columns without all the spaces and tabs that preceed its entries. Then you can copy and paste it cleanly elsewhere in Word or InDesign and use Convert Text to Table to make a real table column of it.
I usually copy the tables into my text editor and do quick search/replaces on the spaces and tabs, copy and paste back into the source Word table. But you can also just highlight an entire table in Word to limit the search and replace and do it in Word.
But you need to be REALLY careful about being sure that you maintain the columns. If there's an empty field someplace, any find/change operation can screw up the table in a hurry.
Place the text into InDesign. Then, run a script from the Script panel named Find/Change By List. Run it on the selected story text.