It may show that the person wants to stop and review some point before moving on in the conversation. 'I have a problem with that (so stop before moving on, so I can take a minute to better understand.)' For instance, 'I have a problem with that being said and...' Thanks
'That' is used here as a demonstrative pronoun, to refer to some thing, some idea, some point. some comment, made earlier in the conversation. It doesn't have to be followed by a noun.