How is a player rated who has similar results against a wide range of players? There is a player I know, whom I would guess to be somewhere between 1600-1800 in strength (call it 1700) who has an unusual profile. 

He's a defensive player who's good enough to beat players 1500 and under most of the time. But he stops beating players as they approach the 1600 level, even though he seldom loses to them. Against players in the 1600-1800 range, he wins 10%-15% of the time, loses 10%-15% of the time, and draws the remaining 70% Against players in the 1800-2000 level his stats are slightly worse, about 15% wins, 25% losses, and 60% draws. His loss rate rises as he plays opponents above 2000. But basically, he gets similar results against people in a (wide) range of 1600-2000.

What are the dynamics of this player's rating? Will he get points for beating 1500 players more often than other 1700 players? Will his ability to draw against players up to 2000 also pull up his rating above 1700? Or will his lack of wins hold down his rating?
The Elo system treats every player as if his expected score against for example -200 -100 0 100 200 points stronger players would be 24 36 50 64 76 percent. If your real expected score deviates from this assumed distribution it just means that the Elo rating doesn't describe your strength very well. 

In a way that is actually the norm and the culprit is the huge drawing range in chess. Stronger players on average slightly underperform against weaker opposition afaik, because drawing with white is just a little too easy. 

In your special case the players rating would fluctuate depending on his opposition without his actual strength changing all that much. If he manages to get a steady diet of 1800-2000 opponents his rating would rise above 1800, if his opponents are between 1600 and 1700, his rating would stay in that range. 

This doesn't actually mean much and it isn't particularly unusual. It's only relevant in team matches or if you need to maximise your rating to be eligible for titles or something.