I am in Australia and have used them via Amazon without problems (other than the cracked jewel case issue from skimpy packaging, which I've learnt to live with), so I tracked them down direct a few months ago and went mad buying up because they're so cheap.
I was getting terrific fills at first - they stated over 500,000 items in stock - and the shipping cost is ridiculously low considering how high the US postal rates (to overseas destinations) are these days.
The only pain was that I could NOT get either of my credit cards verified (has NEVER been a problem anywhere else), so am having to use PayPal. Nothing wrong with PayPal per se, but Import CDs charge you in full at the time of ordering when you use that method. Over the last couple of months I've found their fill rates dropping, which means I am consistently overpaying. I then have to request a refund because under their system an item is automatically cancelled if it's not filled in 21 days.
They seem to have changed computer systems recently. This has resulted in bizarre multiple advices of shipments and the online record of the status of my orders lagging way behind the fact. This all makes it difficult to know whether I will get back-ordered items or not. Orders now tend to be filled in bits and pieces, as other users have noted here. One large order I placed in December appears to be corrupted, as I simply cannot access it online. They may also be having trouble accessing it as they haven't refunded me for the outstanding items I ordered in December or responded to my request for the refund.
This morning I see that they are stating there are just 136,000 items in stock, so there is something going on with Import CDs / CD Listening Bar / Super D International / whatever.
So ... right now I'm wary of placing further orders with them and am going to have to work on them to get my money back on the cancelled items, of which there are quite a few.
By the way, sometimes I've added a CD to my cart, only to find it has a red note stating that they are unable to ship it to my address. When this happens, I invariably find them (Import CDs) selling the same item on ebay - at approx. the same overall cost - and I get it that way. Interesting and worth noting for other overseas buyers.