What did the Israelites do to get God angry?

Answer 1

1) They complained on a few occasions; chiefly in Numbers ch.13 when it seemed that it would be unsafe to enter the Holy Land immediately.
2) When it appeared that Moses had died unexpectedly, they took an unlicensed initiative instead of seeking God's counsel (see Exodus ch.32). This resulted in the construction of an unpermitted image, the golden calf (ibid).
(However, the following should be borne in mind:
The Golden Calf (Exodus ch.32) was quickly and decisively stamped out. And while it was a serious offense, it may be a bit less of a puzzle if we consider the following:
1) It seemed that Moses had died (Rashi commentary, Exodus 32:1); and they wanted something or someone to lead them. They felt that this (seemingly) drastic circumstance justified quickly taking unusual measures.
2) They had a tradition that they would eventually build an edifice to God (Rashi, Exodus 26:15); and, not yet having been commanded as to the details of the Tabernacle, they thought that they might now improvise.
3) The actual intent was not so much to worship the Golden Calf itself, but to worship the Presence of God (Exodus 32:5) which (they hoped) would dwell upon it.
4) The entire event was instigated by Egyptians (Rashi, Exodus 32:4) who had recently joined the mixed multitude (Exodus 12:38).
5) Those who sinned were, at most, in the thousands (Exodus 32:28). Not hundreds of thousands.
6) That generation was judged by an exacting standard, precisely because they were on a high level (- Rabbi Yehudah HaLevi).
7) In each era, there are different spiritual tests. The (main) test in ancient times was whether people would succumb to the lure of idolatry and its preludes. This powerful lure has since been emasculated (Talmud, Yoma 69b), so it is hard for us now to fully comprehend.