I'd like to know whether "that's" should have been replaced by "that was" in the following. The experience took place in the past.
I tried Mary's muffins last Friday, and that’s one of the worst experiences in my life.
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"That's" is a contraction of "that is".
So, your question is really about the difference between "that is" and "that was".
"That was a bad experience" would mean you were referring to a past experience that happened.
"That is a bad experience" would mean you were referring to something you experienced, but can/may be experienced by anyone else at any time.
It is clear from the wider context of your example that the first person is talking about a past experience in their life, and saying it is your worst to date. For that reason, "that was" is the correct choice.