"Baby's First Christmas" marks the final appearance of Sloppy Smurf.
In "Beauty Is Only Smurf Deep", Periwinkle asks her magic mirror who's the fairest in the world, similar to various media like Snow White and the Seven Dwarfs (1937) and Coal Black and de Sebben Dwarfs (1943).
"Baby's First Christmas" has its music reused the most in future episodes, particularly the cue where Mr. Nicholas is not going anywhere being used in some episodes of Season 4, Season 5, Season 6, multiple episodes of Season 7 and 8, and Season 9.
The title of the episode "Beauty Is Only Smurf Deep" is an allusion to the saying "beauty is only skin-deep," which means that while someone may be beautiful on the outside, their character--what's inside, and more meaningful--isn't necessarily attractive.
"Baby's First Christmas" is one of the mainstream media Smurf stories that invoke the "Exposed to the Elements" trope mentioned on TV Tropes, as the Smurfs hardly wear anything heavier than a scarf to protect themselves from the wintry weather.