Berne is a very safe place with nearly no violent crime. However, as it is the capital of Switzerland, it sees political demonstrations every few weeks on a variety of subjects, occasionally leading to police intervention.
The central railway station often hosts drunks and vagrants at night, which is a nuisance but in general not dangerous.
Recently there has been a slight increase in violence from young people. Try to avoid groups of drunk teenagers that look suspicious and you should be fine.
While police officers in Berne will happily help you out if you are in trouble or need information, they are also known for approaching "suspicious" persons in order to check their papers. This procedure is annoying, but legal as you will probably have a hard time proving you were not acting suspicious. Carry a photocopy of your passport and your onward ticket with you, stay calm and polite and you won't have much trouble.
talk
The main language spoken in Berne is Bernese-German, a Swiss dialect of the Alemannic language, although most people also speak German. Alemannic is mostly a spoken language, but also used in text messages etc. In official publications and announcements, German is used.
English seems to be supplanting French as the favorite second language of the Bernese, even though the canton of Berne is a bilingual German and French speaking canton. However, many people you encounter as a tourist will be able to speak both so it's certainly worth a try.