CY1 bridges the high voltage & low voltage sides. Needs to be a quality cap with a proper rating. HKJ asked about its markings earlier in the thread.
OK, here are photos of the first charger (350mA from Tmart):
Backside of board:
And a closeup of that cap.:
As you can see, it reads "102/1KV". So how is that? Any additional concerns?
(I'm going to see if I can replace that first pic with one in better focus (I'm only using my phone) - be right back. EDIT - Done.)
Thanks,
-Garry
Yes, it is not a safety capacitor.
On the mains there will sometimes be spikes with very high voltage. One of these spikes can punch through the isolation inside the capacitor.
A safety capacitor is guaranteed to fail open, i.e. there will not be a direct path from the mains to the usb and charger wires.
A non-safety capacitor can fail shorted or open, it is undefined. If it fails in shorted condition you got mains on the usb and charger wires.
I see. So this charger is still "not recommended". (So does this mean it's "CE" on the label on the back of the case is bogus?) I would ask what capacitor I could replace it with to make it safe, but I don't think this 350mA charger is worth the effort - the 600mA might have been. Any photos of what a proper labeled capacitor would look like or how it would be labeled?
I think I'm just going to bite the bullet and buy an Xtar SP1 from RMM. I just feel that price is a little high for a single bay charger and the price on the dual bay is crazy high! At the same time, I'm tired of throwing my money away trying out these cheap Chinese chargers! At least I will be charging 4.35v cells safer and more properly.
Anybody want to buy 5 cheap Chinese 4.35v chargers? 
Thanks,
Garry
I think I found what you mean by "safety capacitor". Something with markings like this:
-Garry
A prober safety capacitor usual looks like this:
Y means it is designed for usage between mains and low voltage and then all the marks from different authorities.
When the capacitor is wrong, there might also be other problems, i.e. the transformer might not have enough isolation.
Ah, I think we posted at the same time. Thanks HKJ!
Now I'm curious what is in the other charger, and I didn't bring it with me to work this morning!
-Garry
It looks like the circuit board has space for a prober safety capacitor.
It is not all equipment that has a capacitor between mains and low volt side, but leaving the capacitor out can give problems with EMC (I.e. noise or jamming of radio equipment).
Well, opened up the other (second) charger and it has identically marked caps 
-Garry
Might it be reasonably safe to use on the line with my computer's UPS with surge protection and line conditioners?