I don't know that that's the case though. Unless Anderson and Welles both knew what the other was doing and were working together in the beginning which I very highly doubt because it just does not seem likely Anderson would go along with that, how could Wells have known what the Bat looked like to go around the house masquarading as him in an exact costume to what Anderson wore?

Sure, that's pretty clear. Anderson is the sociopath "Bat" who has been killing women since the previous year, while Welles is the copycat "Bat" looking for the million dollars. Note the tense, Mexican standoff between the two of them all the cryptic innuendo whenever they encounter each other.
Anderson, of course, usurps Welles in searching for the million when he discovers Welles' theory about its being hidden somewhere in the house. That's why Anderson kills Welles (and why Welles arrives unsucessfully prepared to encounter him and kill Anderson first.)

I agree with you on that assessment. It would explain why Dr. Welles had the wound on his neck. (I didn't buy the car accident.)

Spoiler:
I think the 'Bat' was two men, Lt. Anderson of course, and also Dr. Welles.

Two bats? Who was the other one?

Actually, after watching this picture several times, I believe there were not one, but two Bats. And they were both killed by end of the film.
To me one of the most exiting scenes is early on, when the bat is let loose into the bedroom and bites Lizzie.

The final revelation of the Bat was also quite exciting; I was genuinely surprised by the Bat's true identity.
I write bios, therefore I am.

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While that may be a good approach to take, anyone who's seen the movie probably recalls this segment when Dale and Judy heard the pounding on the floor above them:
Judy: Shall we call Miss Van Gorder?
Dale: She'll hear it, how can she help but hear it? Besides, we don't want her to think we're a couple of hysterical women.
I don't know, maybe today you have less of a problem with being seen as hystericalback then characters, including women in the movies it seems, were given something of a calm manner to them. They weren't too fond of being seen as crazy because if someone thought you were just plain crazy, they wouldn't take you as seriously.

I wouldn't be in the house in the first place. If I knew a dude with no face had been terrorizing the place a year before, and one night a dude with no face came to the house, I'd be out of there as soon as possible! And this attack happened like, what, one or two nights since their first attack (I haven't seen it in a while).
And I have heard noises and gone looking, but I always took some sort of a weapon with me (i.e. baseball bat). That's when I didn't know that a prowler was on the loose! If I knew, and I
had
to go up the stairs, I think I'd at least get Cornelia and her gun to come with me!
In the tiki, tiki, tiki, tiki, tiki room!

That may be true, but come on, if you heard someone pounding on something on the floor above, and didn't know what was going on, and didn't know if maybe something would fall through the ceiling, would you stay put? Besides that, Dale had a reason to looking, she wanted to see if the stolen money that had gotten her husband put behind bars, had been hidden in the house so they could find it and get him out. Being a wife and having her husband put away for an alleged crime, she probably had more of a reason for looking.

I guess I would say the most exciting scene is when the two girls go up the stairs, and then they see the bat, and then they run down the stairs, and one gets killed. Having said that, though, I don't think any scene in the movie is really exciting. It's hard to get excited when if they just were smart and stayed in their rooms they'd be fine.
In the tiki, tiki, tiki, tiki, tiki room!