The start of this episode has many inconsistencies in the first two minutes. When Dorothy is on the phone trying to get Sinatra tickets she said Stan got her tickets for her birthday, but then asked her for a divorce. In the other episodes from Season 1 (and beyond) she says Stan left her after 38 years of marriage (and didn't ask for a divorce, just had his lawyer call).
The first problem is she says Stan got the tickets, she got the house an kids. Her kids are 25-30 at this point, so she wouldn't have "gotten the kids" because Stan just left her within the last couple years as noted in the episode "Stan's Return" also from Season 1.
Also, if Dorothy got the house why did she have to move in with Blanche at the start of the series?
When Blanche goes in to talk with Dean Cooper, they shake hands and introduce each other before sitting down. At that point, Blanche says she has something important to discuss with him, and he asks if it can wait until the following week, when he's less busy. If he wasn't able to speak with her then, why would he have invited her to sit down and talk?
Goof: Near the end of the episode, Blanche says, "Dean Tucker was no help whatever." I think that "whatsoever" was the word she meant to say.
In another episode, Family Affair, Blanche explains she was thrown out of college after she was caught in bed with a man during bed check.
Professor Cooper: I'm all ears!
Blanche: (suggestively) Don't sell yourself short.
Sophia: You're lucky I was with you. You'd still be in the slammer if I hadn't fake that heart attack.
Rose: My life will be ruined if this ever gets home to St. Olaf.
Dorothy: What'll they do Rose?! Revoke your ice fishing license? Take back your helmet with the horns? I mean, I'm the injured party. Obviously I'm destined to never see Frank Sinatra face-to-face.
Rose: (angrily) They're called longenhergan.
Dorothy: What is called longerhergan?
Rose: The helmet with the horns.
Dorothy: Don't start with me, Ma. I've had a very rough day. The only scalper I could find had strange things moving around in his hair, and he wanted to bargain in a dark alley.
Sophia: So what seats did you get?
Dorothy: I didn't get any tickets! I didn't think it was exactly safe.
Sophia: I can't believe you were such a baby. In Sicily, we did all our bargaining in dark alleys! How do you think I wound up with your father?
Blanche: Dean Tucker, my name is Blanche Devereaux, and I have something extremely important to discuss with you.
Dean Tucker: Can it possibly wait until next week? I've only been Dean here for a few days. I don't have a secretary, I can't get my parking validated, and I don't even know where the restroom is.
Blanche: I was sexually harassed by Professor Cooper.
Dean Tucker: Oh, don't do this to me!
Rose: Here we are, Sophia. The perfect after-dinner treat: a nice dish of jello!
Sophia: I hate jello. If God wanted peaches suspended in mid-air, he would have filled them with helium!
Rose: (helping Blanche study) Whose theory states that a young man has romantic feelings for his mother to get even with his father?
Blanche: I don't know who said it, but my second cousin Arlen did it!
Rose: (disturbed) I think we better try another question......
Blanche: Well, I am devastated--just devastated!
Dorothy: Blanche, what happened?
Blanche: I went to talk to my professor like y'all told me to, and he told me that the only way I'll pass his class is if I sleep with him.
Blanche: Oh, yes! I just don't know what to do.
Sophia: Get it in writing!
Rose: Sophia, why are you in such a bad mood?
Sophia: Forgive me, Rose, but I haven't had sex in fifteen years and it's starting to get on my nerves.
Professor Cooper: (after Blanche finishes her final exam) Well, it looks like we're finally at the crossroads.
Blanche: Whatever do you mean?
Professor Cooper: I mean that I know you've been having trouble in this class, and I'd hate to see you have to repeat it.
Blanche: You know, Professor Cooper, I've thought a lot about what you said, and I have no intention of repeating this course.
Professor Cooper: (gets closer to her) Good! I'm glad you've decided to take me up on my offer.
Blanche: Oh, I'm declining your offer, but I do want to thank you.
Professor Cooper: For what?
Blanche: Well, thanks to you, I studied all day and all night, and whenever I felt like giving up, I thought about you and the kind of man you really are, and I studied even harder. In fact, you made me so mad that I decided to get an A on this test, come hell or high water, and I think I did. I, sir, am a lady. Maybe not the smartest lady in the world, but I do know that my self-respect is more important than passing your damn course, so you, sir, can kiss my "A!" (hands him her test and walks out)
This episode marks the first time we hear Rose talking of her old home town of St Olaf.
The background shot during the closing credits features the four ladies on the couch after Dorothy, Rose and Sophia arrive home from being arrested, listening to Blanche's story about her exam.
Jerry Hardin would once again appear in a 4th season episode Little Sister as the man that Blanche is seeing.
Dorothy: It's different for kids these days; they have Barbara Walters to look up to.
This is a reference to the slight speech impediment that hugely popular television newswoman Barbara Walters overcame (but not without getting made fun of a lot for it). This problem caused Walters to pronounce her "R's" like "W's," which is what Dorothy does at the end of the scene, when she tries to say "Rhode Island."