While Too Many Suspects had been the pilot movie for the new Ellery Queen series, aired in the spring, "The Adventure of Auld Lang Syne" was the first episode of the show as a regular production. It aired at the start of the 1975-76 TV season, in mid-September. (September 11, back when it was just another date.) And it takes place on New Year's Eve.
This is an odd choice, one of a few the episode makes, some of which work better than others. Television programs, at least American series with their longer seasons, do their best to sync holiday episodes with the actual calendar. Characters give out Halloween candy in late October, sit down for Turkey in November, do romantic shit in mid-February, and so on. Since reruns and holiday specials take up the last few and first few days of the year, a New Year's "episode" is likely to be the last three minutes of a Christmas episode, airing a week or more before Christmas. But as one of the suspects in this episode says, "Out with the old, in with the new." If Ellery Queen was a retro whodunit set in the immediate post-WW2 years, it was still a new venture, and the writers may have liked the optimism of the countdown to a new year. (1947, for the record.)
The New Year's setting makes for an unusual structure for the mystery as well. The victim, who we'll get to in a bit, is killed at a bash in the Astor Hotel late into the night. Inspector Richard Queen, Sgt. Velie, and Velie's wife are at the party. (The fact that Mrs. Velie is on the larger side is played for laughs, but it's also made clear the veteran couple are still crazy about each other.) Ellery, on the other hand, has spaced on the whole thing and is on the way to that other tradition: staying in and sleeping through the ball drop. It's only when Velie goes to the Queen apartment and shakes him awake that he even tries to get involved in the case. Since he's mailed his car keys - don't ask - he needs to rouse a cab and get through clogged New Year's Eve traffic, while making stops at a florist and the flat of a girl he stood up, who sounds like she skipped the champagne and went straight to bourbon, and whom we'll never see after this episode.
So what we have here is a story that sidelines the title character for most of the running time. During that time Inspector Queen and his men interrogate suspects and keep all the guests from leaving, while also dealing with the political fallout from keeping a lot of the city's bigwigs around when they don't want to be. There actually is at least one precedent for this in the book series. In 1968's House of Brass the widower Richard Queen gets remarried and goes on honeymoon upstate, where his and his new bride's host manages to get murdered right quick. Ellery is only physically present in the first and last chapter, the latter of which sees him solving the crime. Which, of course, he does here as well.
Of the victim, Lewis Halliday, I'll say that he might not be the worst victim we encounter in this feature, but I'll be very surprised if I see one more unpleasant. He's a fairly standard figure, a rich man who announces his intention to change his will and disinherit everyone, thus sealing his fate. In fairness, most of the relatives and employees he gathers here do come off as pretty slimy. A couple don't, though. It doesn't matter, he abuses everyone, and in a harsh voice that makes him sound like an overheating Dalek. If there's a remote chance he won't be murdered before the end of the night he seems determined to stamp it out.
As indicated above, Ellery Queen comes up with a solution minutes after arriving on the scene. It's a rather ingenious one, and shows a lot of style in the execution. It might have also pissed off some of the audience, since coming to the right conclusion requires knowing about New York telephone exchanges in the 1940s. By 1975 I suspect a lot of the needed expertise was in Miami Beach retirement communities.
There's some good characterization in this episode among minor characters, too small to be considered suspects. The cabbie (Herb Edelman) who Ellery bribes into taking him to the hotel is a likable presence. And the man (George Wyner) whom Halliday not-quite-accidentally calls with his last breath adds a nice human element to the story.