I use a Mac with a prehistoric browser and for several years I have been quite content using Gmail's "Basic HTML view" stripped-down version for non-supported browsers. A couple of days ago there was some sort of big change. The interface looks different (a much bigger font, for one thing), and at the top of the screen the message is gone that used to say "For a better Gmail experience use a fully supported browser." I can still log in and read text messages, but attachments won't open, I can't mark spam or mark a message as read or unread. All that I can do is read text. Nothing else that used to work is available any more. This has been going on for almost three days. Does anybody have an y idea what has happened? Is it part of a temporary shakeout of some sort, or do I have no choice but to change browsers?

A clarification – when I wrote in my initial post that I could only read "text messages" I meant the text portion of emails (as opposed to attachments). I did not mean SMS messages.

For your own sake, use a secure and updated browser that supports standard HTML.

I know what you mean, although I use a different, ancient and very odd browser on a PDA in Basic HTML mode (whose rendering engine is quite up to the job of displaying pre-Web 2.0 pages).

Gmail constantly changes/ adjusts and experiments with the client, that's why it is still in "beta". Sometimes the changes for the worst at end-users' end aren't obvious to them, simply because of too many variables involved in checking beforehand for every potential os-browser-memory-plugins-whatever combination. I am quite sure, however, that, before executing any changes, they test them against a vast, but still limited, subset of such hardware/software instances.

Do this first: flush your entire cache, cookies, the lot. Then reinstall the same browser sans any plugins etc. Quite other programs, restart, run Gmail, and DOCUMENT the outcome, preferably with screeshots (Shift-Cmd-3 ;-)). If the malfunctions persist, contact Google, and wait until they figured it out.

Some of my past reports of issues not dissimilar to yours have in fact been dealt with within reasonable time; others got corrected after a while, a couple of weeks?, without my even reporting them because, obviously, I realized that Gmail would soon come to its senses that recent changes weren't much beneficial to its core functionality in specific settings. An example of the latter:
http://blogoscoped.com/forum/150219.html