(a company's) customer service

"Customer service" is the name for the group of employees in a company who answer customers' questions, listen to their complaints, and help them out with problems. In large companies, it's a separate group with a special telephone number that you call if you need help.

Here are some situations in which you might call customer service:

• You got a telephone bill and the charges were a lot higher than usual. You don't think you should have to pay that much.
• You want to cancel your subscription to a magazine.
• You ordered a book on the Internet two weeks ago and it hasn't arrived yet. You want to know why it hasn't come.
• Your TV isn't receiving any cable TV signal, so you can't watch TV.

"Customer service" also means whatever actions a company's Customer Service group does for you. So you can talk about customer service as a group of people, or as a thing:

Customer service is always super helpful whenever I call.

They didn't even offer to replace it? That's not very good customer service, is it?

(something) leaves much to be desired

If something "leaves much to be desired", it means that you're not satisfied with it. You didn't think it was good enough:

Their pasta leaves much to be desired.

You're an intelligent young man, but I must say that your work ethic leaves much to be desired.

This set phrase is used in formal English. It's pretty common in written reviews of things.