Question: Say you are working in an office where English is not a native language for people but some English terms are used very often (e.g. an IT department). And your boss always pronounces English terms incorrectly.

The question. Is it appropriate to pronounce the terms correctly when speaking to the boss or one should use his wrong pronunciation for any reasons.

It seems to me a bit uncomfortable to use the fixed pronunciation just after his incorrect wording (right in the next sentence). He may find this offensive I think. He may think that I'm either too dumb to remember how it's pronounced after one second after his saying or I'm trying to teach him.

P.S. Trying to tell him how it's pronounced correctly is not an option. Please avoid this advice. Thank you.

Answer: 
As long as you are not gratuitously using the words, you should always aim at correct pronunciation. Knowingly imitating an incorrect pronunciation is dishonorable and groveling behavior. Correct behavior is to pronounce words correctly and ignore other people who may be pronouncing the word incorrectly.

The only thing to avoid would be unnecessarily using a word you know to be pronounced incorrectly by someone else. Repeatedly or unnecessarily speaking such a word could be construed as an attempt to humiliate the other person. Therefore, you should only use the word when absolutely necessary and avoid using such a word needlessly.
First and foremost, **you don't need to correct every mistake**. Focusing on his pronunciation is likely causing you to miss some of the message he is trying to communicate to you. 

If your manager interacts with other English-speaking professionals, you would be doing him a favor by helping him learn to pronounce things correctly. Pronounce things correctly yourself, even if he just pronounced it incorrectly in the previous sentence. It will be subtle, but over time it might work. **Of course, you need to be absolutely sure your pronunciation is correct, too.**

If your boss thinks he's right and you're not, your response might be something along the lines of, *"Oh? I've always pronounced it this way. Let me go check it out and see if I've been doing it wrong."* Then you can double check and let him know what you found.

In the end, it's not the end of the world to mispronounce things, except when the mistake could lead to an entirely different understanding of the speaker's message. In that case, it's good to repeat back what you heard, so he knows you got his message.