I have now tried installing a fresh WordPress site on PHP 5.4 and Types plugin on another place and everything works fine. So it doesn’t seem to be a problem with Types and 5.4 per se.
I wonder if it could have something to do with slug names or perhaps charset or encodings? For some old reason the char set is “latin1_swedish_ci” so maybe there’s something there? I then tried to change all “weird” letters in wpcf-custom-types option to standard ones but same problems occur.
Also for you to know, when accessing edit.php?post_type=myposttype
on PHP 5.4 WordPress tells me “Invalid Post Type” as if it doesn’t exist anymore.
If I downgrade to 5.3 everything is back to normal.