The General Public love Comic Sans, Designers do not...
I think when you are educated in something (anything!) you notice things more; such as the way it's been made, the font chosen, colours chosen, why those choices have been made and essentially whether a design works or not. As well as education, experience is probably a huge factor so we as designers are generally more aware of what makes a good design and what doesn't.
The general public probably don't realise how much work goes into design; just walking around shops they probably are paying more attention to products and prices rather than thinking 'hmm someone had to design that, and that, and someone chose that image, but someone else had to photograph it, and someone else had to edit it'. The general public probably have a basic knowledge of what they personally like and dislike, but in terms of 'understanding' design it depends what you mean.
The General Public may not understand how a design is made or what works, but if they are buying a product or taking note of an advert then they are obliviously showing that that design works as they have been drawn to it.
The General Public are like dogs; not necessarily stupid, but we as designers can train them and make them do what we want with design.