How to add notes/tags to specific times while watching a video?
This seems possible in Adobe Premiere Pro (CS6 at least).
From your question I understand you want to do three things, I will treat every one of them separately. The steps can be used to achieve your goal.
First, open a new project in Premiere Pro (PP) and import the media you want to add comments to.
Additionally, I found the Metalogging window lay-out convenient for this task (Windows -&gt; Workspace -&gt; Metalogging or Alt+Shift+6), but you might find another lay-out fit your needs better.
1. Play video at 1.5x speed
Double click the video you want to play, it will open in the Source panel.
Press Spacebar to play the video and use the L key to increase the playback rate and the J decreases it (credits to this answer).
2. Create a list of tags during playback
While the video plays hit the M key to create a Marker at the timecode currently shown in the Source panel (markers pointed out):

Make sure the Source panel is in focus (i.e. has a yellow line around the panel):

3. Add comments to the tags without pausing the video
Make sure the Markers panel (Window -&gt; Markers) and the Source panel is visible (Window -&gt; Source).
When you add markers during playback, these will show up in this panel with a comment field:

While the video plays, you can add markers in the Source panel and then add comments to these markers in the Markers panel. The video is not paused.
In your comment you mention you would like to export the markers to a file. Unfortunately I did not find a straightforward way to do this in CS6, however, PP Creative Cloud does have this option according to this tutorial.
The option can be found in File -&gt; Export -&gt; Markers and allows you to export an HTML file of your timestamped markers, including comments and a screenshot of the video at that time.