What's eating my Areca palm?

Hello all,
I'm new to houseplants and got my first Areca palm a couple of weeks ago. I have noticed a few holes in the leaves like someone very tiny is having a munch. I've been spraying with pyrethrins, but the damage seems to be getting worse. I can't see any bugs on the leaves or stems, there is no sticky reside or webs. But now a few of the leaves (fronds?) have turned yellow and some have turned brown/black! So something is up. When I lay on the floor beneath the plant and look up under the leaves, I can see what appear to be tiny white specks, which I thought at first were holes letting the light through, they don't move or wipe off.

The stems have lots of tiny black spots (don't move and don't wipe off), but I read this was normal for Areca palms (i.e it's not scale).

Any ideas? Spider mites? If the pyrethrins isn't working, what do I try next? Washing up liquid in water spray? My bedroom is normally about 60% humidity, and the palm is situated in front of an open south-facing window, so there's plenty of air flow and it's not getting scorched. I was spritzing it with tap water, but have now switched to rain water after reading it is sensitive to fluoride.

Thanks in advance!

 

Would be nice to see a few pictures, difficult to comment without actually seeing.

 

I was having trouble getting the white spots/flecks to show up on camera. They're much more visible to the naked eye, but when pictured look like dust orbs.
You can see the holes in the first picture; *just about* see the white bits in the second picture; and the third picture is the speckled stem (would like a second opinion on that one!).

 

Here's a closer look at the stems (just in case it's not normal!). It's a camera phone, so it doesn't do close up very well :(.

 

Gave the Areca a good spray last night with washing up liquid + water. This morning I found a few white specs on top of the leaves that hadn't been there before (still very tiny, but there was ONE that looked wide and flat), these DID wipe off, with the big one leaving a chalky looking trail where I rubbed it. Could they be mealy bugs? There were some other bits of white on the stems pictured below. I rubbed them off then sprayed again with pyrethrins.

 

Not sure but the stem markings look normal.
You will get odd bits on the leaves that show signs of age, maybe a dry atmosphere for a while showing as dry leaf tips.
Cant see any mealy bugs,.
Have you got a hand lens?
Sometimes they show up the smaller pests

 

I don't have a hand lens unfortunately :(.

There's definitely something up. A couple of lower fronds have yellowed and another turned brown and dried up. The beginnings of new canes growing in the middle of the plant start out green, but then the tops turn brown and stick-like. Now immediately this would suggest not enough water perhaps, but the soil is dark and moist and in fact there is evidence of decay. In fact when pulling out the dead and dying fronds (which came out very easily), the base of the canes had rotten. I actually haven't had the need to water it more than once since I brought it home on the 24th July as the soil has remained moist (I have been spritzing the leaves though). So now I suspect that perhaps there's some root rot (or perhaps rot at the base of the canes) and this was the case from the day of purchase.

It's still in the pot it came in as I read Areca palms don't like to be re-potted and do better a little under potted, and since the soil is staying moist and there aren't roots anywhere near the surface/sides, it seemed wise not to re-pot unnecessarily. Of course, this means I haven't been able to inspect the roots or inner soil for problems.

I did take it out in the garden for a little rain shower today and had a little tug to see if it would lift out of the pot so I could have a look. It wouldn't budge and since it's a bunch of canes instead of a trunk/one big stem like other plants, I was scared pulling too hard would just uproot one or two canes and cause damage.

I had a little dig around the top inch of soil with my finger. I discovered something tiny and fast moving-a tiny spider (or mite?) I think. I also found a little long swirly shell buried in the soil! There were quite a few little bits of decaying cane sheathes in the soil too.

The existing established fronds still look green and healthy at this point (although the tips have browned in places due to use of tap water which as I said I have now stopped), so overall the plant looks healthy (at least from a few feet away!). But the gradually dying lower fronds and browned stick-like new growth suggest otherwise! So...is there a solution? Re-potting? Or is the plant just going to eventually die?

Thanks for any advice!