You really ought to have a sense of the old dynamics of the Third Doctor, Liz Shaw, and the Brigadier to enjoy this short story. If you do, this short story does a lot in service of those characters, most particularly Liz Shaw.

I've always been a bit frustrated by this companion as she is fun on paper but lacklustre in action. As a scientist Liz could have been a very fun companion for the Doctor to work with during the UNIT days, especially with the Doctor so thoroughly stranded on Earth in her time. First Christmas is great at addressing that a bit and putting in room for Shaw's character, however briefly, to shine a little bit.

The story is simple enough with the Doctor and Brigadier fighting, while an alien ship threatens to crash on Earth. The Doctor manages to solve both those problems and more in a quick bit of writing, but why the story has significance is that touching ending with Liz Shaw, which is just a nice treat for fans. As a Christmas short, this works well as a straightforward bit of fun.