““molad is not an astronomical observation, but simply adding a fixed average lunar month time that may be hours off a “real” rosh chodesh”
Potentially days off. The only rosh chodesh that is directly tied to the molad, is rosh chodesh Tishrei (better known as Rosh Hashanana).
If the molad occurs in the afternoon, , R”H is pushed to the next day. If the next day is sunday, Wednesday or Friday, R”H is pushed yet another day (Lo Adu Rosh)
so If the Molad occurs 12:01 noon on Shabbos. Rosh Hashana (“Rosh chodesh tishrei” ) will not begin until the start of Monday (ie sunday night) over a day later.
Molados of Teves and shevat in particulary can be off by a long time, over 2 days potentially
(Of course even if the molad was exact, Rosh Hashana/rosh chodesh Tishrei occured on the day of the molad and an eclipse occurred, still wouldn’t recite Hallel on that day)