Two different issues, so I'll comment on each seperately:
Memory: Keep in mind that its hard to directly compare memory utilization with other browsers. Opera is specifically aimed at having an extremely low memory profile, as its used on cellphones and other 'thin clients'. Internet Explorer hides vast amounts of its memory use in shared libraries that Windows loads on startup, which also gives it an unfair advantage on launch speeds.
With that said, My firefox memory usage varies from 25-100mb of memory, depending on plugins, addons, and length of use. I've had it open with 10+ windows, multiple tabs in each for multiple days and never gone above 100mb. However, I do have some tricks up my sleeve. First and foremost, I disabled Java on Day 2 of using it. Sun (in its infinite wisdom) decided to remove the ability to right click on the java icon and remove java from memory after using it. Worse, the latest plugin interface with FF seems extremely buggy, causing my memory to skyrocket, and my browser to crash.
With Java disabled, flashblock, and the web developer toolbar plugin, and nothing else, I haven't had a single browser crash in months, and haven't gone above 100mb of memory used - ever.
Which brings me to issue #2..
Stability: Most of the descriptions fit my experiences with FF before flashblock and disabling Java. Since I did both, I haven't experienced one crash. Trust me when I say I abuse the poor browser, extensively. My suggestion is to start disabling plugins until you find the cause. Start with flashblock and disabling Java. Then move on to removing Quicktime, and if you still have issues, file bug reports on Bugzilla.
I'm not blaming the users here, but my vastly different experience is (I hope) a roadmap that you can follow to get different results.
Personally, I find FF to be the most stable browser I've ever used. Granted, the plugins are a bit wonky, but I personally hate most of that content anyway. Your mileage may vary.
UPDATE:
Some rather visible bugs in Firefox itself resulting in memory leaks have been fixed, which means 1.5 really is noticably more useful over an extended period than 1.0.x is if you keep tabs open or so on.
Plus Fastback is in, which makes navigating between cached pages instant.
The beta of 1.5 is due out today, and apparently, it deals with exactly the memory issue described. When it comes out, grab it and test!