Unlike many here, I'm not very enthusiastic about most of the line-up.
The alternatives, however, weren't very inspiring, either -- with the clear exception of Madeline Kahn, who should have started a three-year run for her comic invention in What's Up Doc? Given the traditionally thankless to-be-abandoned battleaxe fiancee role, she spun it into something wonderful -- in fact, the interplay betwen her and Austin Pendleton looked alot more fun than what was going on between Streisand and O'Neal. As for why she wasn't nominated...while the film was an enormous financial success, it was dismissed as too trivial by most critics, esp. as followup to Bogdanovich's very serious Oscar contender of the previous year. I found the movie extemely funny, but many people I knew thought it was of the Mad Mad World loud-not-funny mode.
Of the actual nominees: I found Pete 'n' Tillie a pretty lackluster piece of filmmaking, and Page's role too broad for my taste. The mystery is how the film got a screenplay nomination over something so clearly superior as The Heartbreak Kid. Was it carryover Casablanca love for Epstein?
It amazed me that, up to Oscar night, Shelley Winters was viewed as a likely winner. The Poseidon Adventure was a joke of a movie to everyone I knew -- strictly for Oscar completeness, a friend and I finally went to see it, and laughed throughout. The idea that Winters might win a third Oscar for it seemed ludicrous. That she didn't was, for me, the only saving grace of the race's actual outcome.
From which you may infer, I think little of Heckart's win. I'd seen Butterflies Are Free on Broadway (suckered in by a Walter Kerr rave, before I knew to dismiss such things), also with Heckart, though Keir Dullea and Blythe Danner in place of Albert/Hawn, and I couldn't stand it. I'd expected something semi-serious, but instead got a typical withdrawn guy/extrovert girl rom-com of the Two for the Seesaw ilk -- rendered even worse by the bourgeios pandering of Heckart's character. Her big moment was her telling off the avant garde director -- a clarion call for all squares in the audience to stand up against the counter-culture. To be brutally honest, I can't even swear this moment survived the film version -- I only watched it once on TV, under duress, and my memory is hazy. But, to invoke the principle others have used in previous years: when I dislike a project as much as I do this one, you're not going to get me to vote for anything connected with it.
Fat City was, at least, a more artistically ambitious film than any of the preceding, but I thought it had that half-hearted, not-truly-engaging quality that for me marked too many second-tier films of the 70s. As for Tyrell...I'm afraid I saw an actress Trying Really Hard, and generally being twice as flamboyant as any actual human being would have been. My feeling when she got nominated was that the line between truly bad and memorable was very thin, with personal taste determining which side of the line you fell.
Which might also explain why I feel so differently about Jeannie Berlin than Magilla professed to in his intro post. I think she's genuinely hilarious, unafraid to make herself absolutely repulsive (check her out making pig with that egg salad sandwich), and then being touching in a totally unexpected, controlled-hysteric way when Grodin dumps her. Clearly she had no follow-up career, after the fiasco of Sheila Levine is Dead and Living in New York, and it's very possible this was the only thing of which she was capable. But, in this crowd, she's the only one to whom I can consider giving my vote.
I can't attest to whether Limelight ever showed up on TV, but I'd point out that, because of the blacklist issue, the film might well have been on a no-show list for a long while. Further, at that time, not all film libraries had yet been opened to TV broadcast, and it wasn't that unusual for some famous titles of pre-TV-era to remain unseen. Wuthering Heights, for instance, only made its TV debut in 1966. So there are reasons to think Limelight might not have been subject to an Oscar ban on the TV technicality.