Your friend is right. "Could you please deal with it?" does sound less polite than "Could you please take a look at it?"
There is a slight difference in meaning between the two phrases that makes one more polite than the other. If someone asks you to "deal with it", they are directly asking you to fix the problem ("deal with it" means that you will take full responsibility for the problem). If someone asks you to "take a look at it", they are not directly asking you to fix it, but are just asking you to look at the problem and assess it. They are also implying that they would like you to fix it, but they are not directly saying that. That's part of what makes it more polite.
In English, being indirect in a question makes it more polite. You also see this in the way that you can phrase questions with modal verbs. Here's an example of ways to phrase a question in order of increasing indirectness (and so increasing politeness):
- "Will you swap seats with me?"
- "Could you swap seats with me?"
- "Could you possibly swap seats with me?"
- "Do you think you might be able to swap seats with me?"
- "Is there any possibility that you might be able to swap seats with me?"
The more uncertainty and indirectness you add to the question, the politer it becomes. In the last example, you aren't even asking whether the person will swap seats, but are technically asking whether it's possible that there is a possibility that they might have the capacity to swap seats with you. Which is...very indirect!
See this article on the BBC website about making questions more polite by making them indirect: http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv239.shtml