While an important question might be 'why you would want to find out?' I can say that I experienced no feeling of danger or limitations on walking about during the day in the capital. I do go beyond the areas with roads. I have felt even more comfortable in my brief travels upcountry.
I can understand how the deep poverty and the naturally out going and interactive nature of Liberians can cause visitors significant discomfort. This is a cross cultural issue. Since I once lived in this country, I do not feel this discomfort.
The UN peace keeping group did say in July 2010 that it felt that there was still a significant risk of small situations escalating into major confrontations. The capability of the police to control these situations leaves much to be desired. Although it seems to me that Liberians are much quicker to physically fight than they were before the extended periods of war, at least recently weapons have not been a part of the fights.
Theft and petty crime is felt to be higher in the capital than desirable, but it is hard to judge how the level compared to that found in the USA or other more developed countries.
My hosts and others advised against walking around the center of Monrovia or on the beaches at night. I had no opportunity or compelling reason to evaluate the validity of this advice.
Though Liberia was a relatively peaceful country when I lived there, it has since undergone about 20 years of civil war and societal destruction. My only "claim to fame" is that, while in Liberia, I had a serious romantic relationship with a Liberian man who now is the Vice-President of the country! Despite this personal connection, though, I would NOT visit the country at this time or at anytime in the foreseeable future. Living conditions are much more harsh and primitive than when I lived there more than 30 years ago.
officials are a little less officious. there are few telephones.little public transport. the country is recovering from a civil war which wrecked the infrastructure. things are looking up. there is a certain amount of street crime in Monrovia and dispossed people can act like bandits in isolated areas;it is generally possible to negotiate a reasonable agreeement and they sometimes become friends.