I have the same problem. After messing with all my calenders, the only change is that the number increased from 1 to 2. I don't know how to get rid of it.
I got it too, the number 1 in the upper right corner of my Dock icon. It is also to the right of my calendar under "Calendars" on the left, but none of my subscriptions?: 😕
I often receive meeting notifications via e-mail. It appears as a little iCal icon at the bottom of the e-mail. Clicking on it will automatically put the meeting on your iCal schedule. It will also put a note on iCal at the bottom left side of the calender and put a number on the iCal icon. Clicking on the note (apparently signifying that you are aware of the new calender item) removes both note and the number on your icon.
All the posts are years old but maybe a new mac user (like me) will come here and need the answer.
I came here with the question "a little red three is on my calendar icon and I don't know why"
I opened the calendar and on top left I saw a three. I pressed the arrow near it and it listed three events. I clicked ok on each one and the corresponding red three on my ical went away.
Apparently it is a reminder-which I actually like.