This thread is a bit old – nevertheless: There are a few classes of English verbs that aren't to be used in the continuous. Verbs related to perception are such a case, so we don't say "I am hearing…", "I am tasting…", etc. The meaning can still be "continuous" even if the form isn't, which is also true of German's present tense. Thus, "ich sehe" is both "I see [right now]" and "I see [on a regular basis]", and "ich koche" is both "I am cooking [right now]" and "I cook [every day]".
That said, "I am seeing somebody" also has a colloquial meaning, namely "I am in an intimate relationship with somebody". So the phrase "I am seeing people" might lead others to think of you as being a bit polyamorous ;-)
Here are some more verbs that you probably won't see in the continuous: believe, doubt, feel, imagine, know, dislike, love, hate, prefer, realize, recognize, remember, see, suppose, think, understand, want, wish, appear, hear, look, see, seem, smell, sound, taste, agree, deny, astonish, disagree, impress, mean, please, promise, satisfy, surprise, belong, concern, consist, depend, fit, involve, lack, matter, need, owe, own, possess, weigh etc.
"Ich beobatche Menschen" would mostly be used if you mean you watch as in study or monitor a group of people. For a more general use you can use "ich sehe Menschen an," which means that you are just looking at them.
To see something is not quite the same as to watch it or to have it as your point of focus.
Der Mench is 'The person' and it is one of the weak nouns that add an -en for direct object. How therefore do we know that the noun is plural here rather than singular with accusative ending?
Because Mensch is countable -- and as in English, countable nouns in the singular almost always need some kind of determiner in front of them, e.g. an indefinite article.
Like how you can't say "I see person." in English -- if it's singular, it would have to be "I see a person." or "I see the person." or "I see that person." etc.