Ok, so, on www.linksysinfo.org there's a lot of very useful information.

Problems I had are known, and there is some newer firmware on Linksys FTP site (and not on the web) that I downloaded and hopefully will fix the problem. It worked with many users, but not all.

So, now, part of the port forwarding function is not working with current official firmware, nor it is the wireless connectivity, which is quite instable.
Frankly, I think this is quite unacceptable. I hate to be a "complainer", and I am ready to accept that marginal, minor features are not working, but I can't think they put on the market a device that would not perform correctly two basic, essential functions such as port forwarding and wireless stability. The fact that I still don't know whether this new release is completely fixing the problem makes this whole thing even more irritating.
And they have a great reputation and they carry the Cisco bran on their cases. Well, was I naive to rely on tech reviews and articles...

Stig, thanks for the link. It is in fact mentioned on the above website, and I also have a WRT54 which is working great, so that will be useful all the same