In a previous life I used to be a reliability engineer. In terms of the
electronic components, there is no harm at all in leaving your laptop on all
the time. In fact thermal cycling (due to switching on and off) seems to be
slightly more harmful.
However, your LCD screen backlight has a finite life, so I suggest you think
about letting the power options blank the screen after 20 minutes (or
whatever you like) of idle time. That shouldn't cause any of those problems
you've had when trying to "waken" it from sleep mode.
The electromechanical components - the fans and hard disks - also have a
finite life. To be honest, though, there's no reason to suppose that they
are any more prone to wear than those supplied with desktop machines, so you
can make your own judgement here. Just remember that when they do wear out,
it's much more difficult to replace them.
You might want to think about letting the disk spin down when blanking the
screen, although there is some uncertainty about whether this slightly
increases the failure risk (thermal cycling again). Personally I'd let the
disk spin down. Saves a few watts of power, too. The fan(s) will slow right
down anyway when the CPU is idling.
Finally, the air passages in a laptop are narrower and thus more likely to
clog with dust, which is another thing that gets worse with time.
So, there is no definite answer, and a lot of this is about judgement.
HOWEVER, I can tell you that my laptop sits in the spare room and is NEVER
switched off. It runs 24/7/365, and has done so for over two years, and is
still in fine fettle.
So my answer to your question is, "Yes, it's OK to let it run continuously,
so long as it's well ventilated and not sitting directly on a dusty floor."
SteveT