Episodes 1-4 aired on Thursday (1, 3) and Saturday (2, 4) to try and maximize exposure and also test different time slots. (By the late '80s, the networks realized they could just have an "encore presentation.")
But this meant HSB was up against either Knots Landing (Thurs) or Fantasy Island (Sat)-- both hit shows, and both with hit lead-ins (Waltons/Magnum PI on Thurs., The Love Boat on Sat.).
For episode 5-12, they stayed on Saturdays... a dead zone for prime time TV.
Episode 13 -- the intended season finale -- aired on a Wednesday, replacing Quincy. This went up against Vega$ (then on its last legs, soon the be replaced by another struggling freshman mid-season drama, Dynasty). That year, NBC had just six shows in the Top 30... and three of them were on Wednesdays, giving HSB just about the best lead-in possible (Real People, Diff'rent Strokes, Facts of Life). At least, they had the best numbers, even if not a great fit for HSB's audience.
Incidentally, NBC's other big night -- Mondays -- had no room since Little House on the Prairie was followed by a two-hour movie (and would have put HSB against another MTM show, Lou Grant).
The other option may have been Sundays, when NBC had CHiPs, but there are several reasons that would have been a bad idea: Sunday night was a bad fit for a gritty drama, CBS' lineup was full of big hits, and even ABC had a movie in the Top 30.
OK, so what about episodes 14-17? Those were ordered later, held for May sweeps, and formed a separate story arc which also introduced Joe Coffey. Those aired as two 2-part episodes on... TUESDAY! The biggest night for ABC since the mid-70s... HSB would have faced Hart to Hart, with a lead-in of Happy Days, Laverne & Shirley, Three's Company, Too Close For Comfort. Sounds like a classic Fred Silverman triple-decker sandwich to me. HSB had no chance. (And neither did Silverman; he left NBC not long after).
