It would be handy to have a Next Comment button - analagous to the Next Game button - that would take you to the next topic you have an alert for.

Currently you have to click on MY HOME and scroll down past the Current Games listing to the New Comments section. (This itself is a great improvement on the olden days - see alert-issue).

What if I prefer to read next the 3rd or 4th comment in the queue line (do not think that I ever used the French word here to illustrate my lengthy arsenal of positions or comment) ?

The dedicated button could be like a toggle switch allowing to move back and forth on the comments, as I may want to reread a comment, and with additional options to skip or just go to the next comment, so a drop down menu would be in order to select my preferred choices.

Buttons where invented for shirts and trousers and now is a common term in computer interface navigation. Just be careful of the buttons that you push.

You can already do this. Click on MY HOME. Scroll down to New Comments (as noted here - for those on the alert).