As per the documentation, print returns true on success and false on error, but errors aren't always detected immediately.

When writing to a file,

1. The data is (possibly) assembled in a buffer in Perl before being passed to the OS.
2. The data is (possibly) assembled in a buffer in the OS before being being slated to be written to disk.
3. The data is (likely) queued to be written to disk before actually being written to disk.

An error in step 1 (e.g. the file handle isn't open) would result in print returns false.

An error in step 2 might not result in print returning false. A subsequent write (e.g. print) or close will return false instead.

An error in step 3 can occur after the file has already been closed, in which case it cannot be reported. On a unix system, one would use fsync(2) to ensure the data was written to disk correctly.

$! will be set by print and close is they return false.

Update: Greatly elaborated to clarify.