Various programmes crashing frequently - could be an issue with the system?

About a week ago Firefox started crashing very frequently, 20 to 30 times a day. On random pages, doing random things, sometimes even when it is minimised. I ran the updates and checked the system for malware with rkhunter. After trying that and a few more suggestions from the Firefox help pages without visible results, I submitted a report to the Firefox Forum.

Meanwhile other programmes such as Eclipse or pgAdmin started hanging occasionally (but not crashing). But this morning Rhythmbox started yielding a similar behaviour: it crashed some 20 times in little over on hour, to the point I had to switch to VLC for audio playing.

Now, before I go through the painstaking process of submitting a crash report to the Rythmbox folk, I would like to understand if there isn't something wrong with the system itself that may be prompting these crashes. /var/log/messages is empty and dmesg shows nothing extraordinary, even though I am not sure what should I look for.

What else could I try to guarantee the system is not struggling with something?

Update

I ran the memory test and it reported a few errors. I got the memory chips replaced and now the memory test passes through without reporting errors. However, applications keep on crashing.

Some python scripts on which I am working right now are crashing with exceptions issued by malloc and free e.g.:

*** Error in /usr/bin/python2.7': free(): invalid next size (normal): 0x0000000001fe7fc0 ***

This morning the hard drive was swapped into another laptop with the same mother-board and the symptoms are exactly the same, with multiple applications crashing and exceptions on memory access. Thus an hardware issue is discarded for the moment.

Solution 1:

Running out of options I decided to re-install the system, this time with Ubuntu 15.04. I have now most programmes up and running and there are no crashes; the system is entirely stable and much faster.

I suspect these issues were cause by some incompatibility of kernel 3.16 with the hardware (Lenovo T420).