In the UK, a perrenial gripe of engineers is to see people calling themselves 'Domestic Heating Engineers'- better known as plumbers or 'Refuse Engineers'- aka dustmen.
The battle to make 'Engineer' a notifiable title (like Doctor) in the UK has been lost, although if people want to they can become registered European Engineers and move from Mr/Mrs/Ms/Miss to 'Euring'. Personally, I don't know how to pronounce it! In much of Europe 'Engineer' (or the equivalent in the local language) IS notifiable- I was called "Dottor Ingineur" while working in Portugal, for example.
Legally, there's also little regulation on who can do 'engineering' in the UK. Insurance companies and certifying authorities are very nervous insuring or approving plant etc that wasn't designed or checked by a 'competent person'. But generally, the only time there's a legal aspect to competency is if there's an accident: if it all goes tits up you've got to show in court that the person who designed it was 'competent'. One of the easiest ways in the UK to proove you are a 'competent person' is to be a Chartered Engineer (which I think is equivalent to PE in the States?). So for example, I became chartered so that I could sign off oil & gas reserves estimates as a legally accepted 'competent person'.
Currently there are two routes to becoming a Chartered Engineer- an accredited degree, followed by a minimum period of professional training and experience, or lots (decades) of professional training and experience on a case by case basis (and maybe passing the Engineering Council's exams too, depending upon the individual and the Chartering Institution- the Institute of Mechanical Engineers is famously strict, for example). There are moves to try and stop the non-degree route to chartered engineer, in an attempt to "raise the status of the engineering profession" (see first paragraph!), by introducing the new professional qualification of Chartered Engineering Technician for those without a degree. At the same time, many 3 year BSc (Eng) engineering degrees are loosing their accreditation: accredited degrees are being restricted to the 4 year BEng or MEng degrees.
As a side issue, in the UK for centuries there were two kinds of medical professional: a Doctor, who'd been to university, gave out drugs etc and Surgeons, who cut people open. Surgeons were self taught, didn't go to university, were called 'Mr' and were looked down upon by 'proper' doctors. Gradually, the two professions linked up, so that now, you start in medical school as a 'Mr' or 'Ms' (or whatever), become a 'Dr' on graduation and then eventually revert to 'Mr' when you become a hosptial consultant or surgeon!!!