Probably too late for you to read this, but perhaps someone else is in a similar situation. That time is about when I went to school, and I can only recall two things that have changed, and neither will actually make any difference to the "result".
The verb form now called "preteritum" was back then called "imperfekt", but the form itself has not changed. And I don't know if this change is even visible if the book is not written in Swedish.
People are now taught two genders, common (en-words) and neuter (ett-words). Back then we were taught four, neuter is the same, but the en-words was divided info feminine, masculine and "reale". Basically the former two are used for persons and animals, "reale" for objects. However, since there aren't (nor was) any actual difference* in the grammar between those three, all en-words are joined into the common gender ("utrum" in grammar-Swedish).
(*The adjective ending -e for masculine words still exists, however (at least today, I don't remember what I learned in school) the normal -a ending can be used on all forms, also masculine. There are also some words with only -e ending for any gender.)
Then there are some new words (the gender neutral personal pronoun "hen" for example), and some things considered very colloquial back then might be more accepted today, though such distinction often depends on the person one speaks too, and what they once learned. Also today the letter "W" is just another letter, it might be described different in that book. Altogether, no big changes (as far as I know).
I'd say there is one common exception. If you see someone by the stove, it is common to ask "Vad lagar du?" for "What are you cooking?". However, without context, that same question means "What are you repairing?". When the context is not clear, one need to ask for example "Vad lagar du för mat?" (~ What kind of food are you cooking?).