I'm getting cache error messages

The default cache directory is ./cache.

Dot-slash-cache (./cache) means that the cache directory is in a location that is relative to the page calling SimplePie – not simplepie.inc itself. Dot-slash-cache is not relative to your root (like slash-cache (/cache) is).

As a simple explanation, the (default) cache directory needs to be writable and in the same folder as your SimplePie-enabled page – not SimplePie itself. For example:

/path/to/mypage.php
/path/to/cache/
/path/to/some/ridiculously/long/path/someplace/else/for/simplepie.inc

You can use set_cache_location() to set the cache directory to a different location. This is particularly useful when you have several SimplePie-enabled pages in various locations and you want them all to share the same cache location.

See Troubleshooting the SimplePie Plugin for WordPress.