This is a fairly common construction in Icelandic. Instead of using the passive as in English (“…a few things that needed to be done”), in Icelandic an implicit “it” is used as the subject of an active phrase: …sem [það] þurfti að gera.
If the construction occurs at the beginning of a sentence, and in some other cases, an explicit subject is used:
Það þurfti að gera…
If it helps, the same construction exists in, for example, French, although in that language always with an explicit subject:
Il y avait encore un certain nombre de choses qu'il fallait faire.
Yes, I think most people would say it's wrong, but I think I've heard it in colloquial speech. There is also a stylistic aspect: it feels clumsy to repeat the word það as a dummy subject within a single sentence.