Can a store show employees a video of a supposed shoplifting case if the suspects have been proven innocent?

If they are defaming you, you may have a legal claim against them. Defamation is the public making of untrue factual statements which damage your reputation. Note, however, that:

1) Showing a video, without comment, and letting people draw their own conclusion, is probably not defamation, unless the video has been modified or "faked" in some way. If the video is unmodified and the people showing it are not saying anything, they are not making an untrue factual statement.

2) Even if they are making what you believe is an untrue factual statement, bear in mind that the fact that you were found "not guilty" (and to technically correct, that is the finding--people are not found or determined to be innocent, but rather they found to not be guilty because the prosecution could not prove guilt beyond a reasonable doubt) does not necessarily mean that they are lying for purposes of a civil lawsuilt. That is because the standard of proof in a criminal case, "beyond a reasonable doubt," is much higher than the standard of proof in a civil case, which is "preponderance of the evidence," or just "more likely than not." Thus, if you were to sue them for defamation, if they tried to defend themselves on the basis that what they said was true (since true facts are not defamation), it is possible they could "prove" that you had shoplifted to a sufficient degree to win the defamation case, even if it could not be proven sufficently to convict you in a criminal trial.

That is not to say that you could not win the case, or should not sue them for defamation, if you feel you are being defamed; it is just a caution that winning a criminal prosecution does not mean that you will necessarily win a civil case. You may wish to discuss the matter with a personal injury attorney in detail, to explore the strength of any case and what it might be worth.

If they are not defaming you, then they can almost certainly do this--the law does not generally prohibit telling the truth--or, for that matter, stating opinions, even every negative ones (opinions, like true facts, are not defamation; only untrue facts may be defamation).

The issue you have here is one of defamation of character. In Michigan, if a person purports false information against you, that causes irreuptable harm or damage to your character, and the person knows this information to be false but maliciously chooses to purport it, then they can be liable for civil damages in a civil suit. Not knowing too much more than the facts you stated, it appears that your were never charged criminally, but rather this matter was handled internally with the store. The store has a right to refuse service to you if you are a known or belived to be a shoplifter, however, if their allegations are false, and they continue to cause damage to your character with information "they know" to be false, then you may be able to sue them to have them stop showing this video and falsely accuse you of shoplifting. I would speak to a local attorney in your area to discuss your various options or you can contact me for more information.