Is it okay to mix tenses in the same sentence? Yes, if what you’re saying is in different time zones.
For example, these sentences aren’t saying the same thing. “Peter told me you were unhappy with the way I handled the meeting.” “Peter told me you are unhappy with the way I handled the meeting.”
The first implies you were unhappy but might be okay about it now. The second implies you’re still not happy.
This is a common problem with reported speech. There’s an assumption that since you’re reporting something which has happened, you need to use the past tense throughout the sentence. Not so.
The rest of the sentence needs to be in the appropriate tense.
Of course, the alternative is to speak like a football pundit who use the present tense for everything – even when the match took place minutes, hours or years ago!
“Donaldson passes the ball to Griggsy but Banes intercepts and flips it over to Wilson who bangs it into the back of the net.”