Yes, but why was Matt Burke so upset that he invited Mike in?
And it’s in this that I think we find the answer to the mystery.
When Matt is telling his story to Susan at his house, he says:
“…And something has me worried…rather badly worried. According to the old literature, a vampire cannot simply walk into a man’s house and suck his blood. No. He has to be invited. But Mike Ryerson invited Danny Glick in last night.
And I invited Mike myself!” (Chapter 9, Section 5)
This establishes that when a vampire is invited in, it doesn't have to be by the owner or a permanent resident of the house. Anyone who is invited in can extend an invitation to a vampire. (It’s like when you throw a party and people you invite decide to invite other people to come. Vampires have no consideration.)
So based on this, once Mark invited Danny Glick in, Danny could, in turn, invite Barlow. I don’t know whether Danny actually had to be in the house to issue the invitation, but he could have easily slipped into the house when the family was away and formally invited Barlow in. Once that happened, Barlow could enter at will, which is what he did.
Matt realized that he had to revoke his invitation to Mike and once he did so, Mike left. As Mark was able to drive Danny away with the cross, he probably didn't realize that his invitation would allow Danny to return.
I conclude that we do not have a plot hole here.