Concern can be a verb, a countable noun, and an uncountable noun. As an uncountable noun it refers to a mental or emotional state - to express concern is to indicate that one is experiencing that state. That can also be reflected by the adjective concerned (which has multiple meanings as well), with a meaning close to (but not identical to) worried.
To express a concern or express concerns is using the word in its countable noun sense, which refers to one or more specific concerns - a concern being particular element or thing to be concerned about. So you might say:
I have one or two concerns with this proposal.
And what you mean is there are a small number of specific things that bother you about it.
A person expressing concern might or might not have specific concerns that they could explain, but if they did, they would be expressing those concerns when they explained them.
If someone is expressing the concern, there should be a specific, already explained or identified concern - a particular thing they are worried about. That wouldn't mean they were expressing concern specifically about the death penalty, but that they had a specific concern about it. So you might use that if you had already talked about people being worried about people executed for crimes they didn't commit - and no other specific concerns.