"countless issues" is correct and usable in written English.
You can use it to refer to a large number of issues or problems that are too numerous to count, often when you don't know the exact number. For example, "The region is facing countless issues due to the recent unrest."
There were countless issues with unions, state inspectors and banks.
It seems Alanis is beset by Countless Issues.
The inquest has shone a light on the countless issues impacting eating disorder sufferers, carers and practitioners".
It goes without saying that there are, of course, countless issues not discussed in this limited space!
After countless issues with banks and the government, they put the business into voluntary liquidation and are returning to Britain.
Devising a phone system that caters to the countless issues that could arise from any of these products — this is a job the Haggler does not want.
On countless priorities – issues that matter to people across the country, regardless of their politics – Republicans in Washington have traded progress for partisanship.
I'm certain there are countless more issues and solutions around this very topic, and I'd love to hear your ideas in the comments below.
Though the Senate has been paralyzed by similar blocking tactics on countless other issues, Mr. Bernanke probably has enough support in both parties to clear the 60-vote hurdle.
There are countless practical issues, all of which are likely to spur intense argument, especially because other Tea Party favorites, like Ayn Rand and Milton Friedman, often disagreed with Hayek (Rand once called him "pure poison") and with one another on fundamental issues.
"They faced countless daily issues — school problems, struggles with discipline, bed times, expectations and a tendency to let things slide a little, which really doesn't work well for kids".
