Some of this is conjecture on my part, but it seems like Rashi commentary discusses why we need all these dates (except Aharon's passing). He seems to be implicitly answering your question.
The first census
Rashi (Bamidbar 1:1) says that G-d often counted the Jews because He loved them. The Maskil Ledavid, in his commentary on Rashi, explains that all the other times the Jews were counted one could argue that it was for a specific need (e.g. after a plague), the Torah here tells us the date the commandment to count was given to show us that there was no specific reason to count the Jews. The commandment was only given because G-d loved them and wanted to count them. (see there for more details).
The Commandment concerning the Korban Pesach
Rashi (Bamidbar 9:1) says that we are explicitly told that this event happened before the events beginning of Bamidbar to teach us that there is no set order to the Torah.
Without the dates given, some would argue that this was not out of order.
The first journey from Mount Sinai
The Gur Aryeh explains Rashi (Bamidbar 10:11) as follows: Why does the Torah tell us the date they left, so that we know it was almost 12 months. Just like a Chatan must stay with his wife during the first year of marriage, so too G-d and the Jews did not travel for the first year (See the Gur Aryeh for an explanation of why they left 10 days early and did not wait the full year).
The Jews arrival at Kadesh (followed by the death of Miriam)
WARNING: This is weak conjecture on my part -- Rashi (Bamidbar 20:2) tells us that we see that the Jews had water all 40 years in the merit of Miriam, since it stopped after her death. However, since Miriam passed away in the first half of the month of Nissan, it would not be before the 40th year started, on the 15th of Nissan, only be 39 years, not 40.
However, we already know that the first Rosh Chodesh Nissan the Jews spent in the desert was called "The Second Year" (Bamidbar 9:1. See Gittin 60B - mentioned in Rashi 5:2 - that this was Rosh Chodesh).
So we can say that Rashi is saying that this is why the Torah tells us they arrived at Kadesh in Nissan, to let us know that they arrived once the 40th year had already started. Based on the principle "Miktzat Shana K'Shana", Rashi is saying that the water was provided in Miriam's honor for 40 years in the desert.
The death of Aharon
I'm not sure about this one. I haven't found a Rashi that discusses the date of Aharon's passing.
Alternative reason why the Torah mentions when Miriam and Aharon passed away:
Zechariah 11:8 says, "And I cut off the three shepherds in one month". The Talmud (Ta'anit 9A) says that this refers to Moshe, Aharon, and Miriam. If the Torah didn't tell us the dates Miriam and Aharon passed away, I might think that they all passed away in the same month.
[Instead, the Talmud says that after Miriam and Aharon passed away, the Well and Clouds disappeared, only to reappear in the merit of Moshe. When Moshe passed away all three disappeared again. This was considered as if Moshe, Aharon, and Miriam were taken at the same time.]