First, I would strongly recommend against using any of the functions from the utf8 module, since these are really only meant for use if one knows the inner workings of how Perl handles Unicode and non-Unicode strings.

That's not true.

utf8::encode and utf8::decode

Safe. Used for efficient encoding and decoding.

utf8::upgrade and utf8::downgrade

Safe. Used for working around The Unicode Bug.

utf8::is_utf8

AVOID. Only useful when checking code for The Unicode Bug. Any use outside of debugging suffers from The Unicode Bug by definition. Use one of the previously-named functions instead.

utf8::valid

Safe, but extremely limited use (as it checks if scalars are well-formed).

It's actually Encode that has the subs you should avoid.

Encode::encode and Encode::decode

Safe. Used for encoding and decoding.

Encode::is_utf8

AVOID. Only useful when checking code for The Unicode Bug. Any use outside of debugging suffers from The Unicode Bug by definition.

Encode::_utf8_on and Encode::_utf8_off

UNSAFE. There are no reason to ever use these, so NEVER use these. Use one of the utf8:: functions instead.
Encode::_utf8_on($s) is short for utf8::decode($s) if !utf8::is_utf8($s);, which suffers from The Unicode Bug by definition.
Encode::_utf8_off($s) is short for utf8::encode($s) if utf8::is_utf8($s);, which suffers from The Unicode Bug by definition.

The Unicode Bug refers to code whose behaviour depends on the internal storage format of a string (i.e. the value returned by utf8::is_utf8 and Encode::is_utf8).