Collocations Use With “problem”, “trouble” & “issue”

1.       The differences in meaning:

The word “problem” is connected with the word “solution”

Some bad things that happen can't be called "problems" because they're unsolvable. For example, if you broke your leg, you probably wouldn't call your broken leg a "problem".

"Trouble" is less connected to solutions. It's more connected to negative feelings that you get when bad things happen.

"Issue" is associated with difficult decisions and disagreements. We use "issue" in a similar way to "problem" or "trouble", but it also has another meaning. It can mean a topic that people are talking about or disagreeing on. Social issues and political issues are examples of this kind of "issue".

2.       Collocation using:

·         "Problem" is used more than "trouble" or "issue". A "problem" is something bad that you have to deal with. 

·         “You "have" problems.” Or “There are problems with “things””

·         "Problems" belong to people, so you can say that something is "your problem", "their problem"

·         You can "be in trouble" or "get in trouble"

·         You shouldn't use articles ("a" or "the") with "trouble". But you can say "some trouble"

·         Things can "cause trouble"

·         Notice that "problems" and "issues" are countable, but "trouble" is usually uncountable

·         You can say that a person "is trouble", which means that they're dangrous or they cause trouble for other people

·         You can use "trouble" with a gerund ("have trouble __ing")

"Problems" can fit into this pattern too, but it's much less common.

·         Say "It's no trouble" when you're politely offering to help someone

·         "Issue" is softer-sounding than "problem". You can use the word "issue" to talk about problems at work

·         If you say that a person "has issues", it means that they are mentally or emotionally unhealty. They may need a psychiatrist's help.

"Problems" can work in this phrase too, but it's not as common

·         To say that you don't like something or disagree with it, use the phrase "have an issue with ___"

"Problem" can work in this way too.

·         When discussing a problem, you can say "the issue is ___" to talk about what the most important part of the problem is

·         You can use "problem" the same way, but not "trouble"

Source: http://www.phrasemix.com/answers/whats-the-difference-between-problem-trouble-and-issue