Something on a syntactical level that you won’t find in Modern Icelandic is loose noun phrases in the subject. For example: “Þór fór fram á leið ok þeir félagar.” Here we see that “Þór“ clearly governs the verb inflection even though his companions were with him, too. In Modern Icelandic you would order all the “agents” in the subject phrase together.
A lot of verbs govern different cases today, or they have been equipped with prepositions to get rid of the genitive governance, for example:
(wait for/await): bíða einhvers has turned into bíða eftir einhverju(m)
(wish): óska einhvers has turned into óska eftir einhverju(m)
+ many similar cases