yeah, it's common to say as a kind of japanese slang.
a delicious part means that suggests what the person in question engages now;
how is the situation depends to answer you.
if he is talking about the guy who is a coworker of talking guy and
the questioning person is said "あいつはいつも、おいしいとこをもってくなあ・・”
if that to say, in thier business, the guy feels overheaded to the person.
if you are friends and talking about a time the person didint come, and talks about his usual conduct in catching a nice girl hunting that his capture is usually amaging,
and usually the Qtioned guy are separated to thier party with getting pair with new girlfriend,
from thier friends, who were together to chatted with girls also but no gain of love hunting..
that's tha situation to use this "おいしいとこもってくよなあ、あいつ・・”
that's the kind of ways to use in popular in young japanese.
いわゆる、ちゃっかり屋とか、うまみだけを持ち逃げする（仕事とかプライベートとかで、仲間を出し抜いておいしい思いをする＝うまく立ち回るひとのことを、多少からかいと、おかしみをこめて、愛すべき態度として笑います。It's a positive way to laughing at the pointed out person. he is almostly cute, and loving to do.
if my english is all small characters use and not correct to teach to anyone,
don't speak ill backyard.
but tell me softly and, polite way to persuade my inrudeness.
I'm domesticated originally Japanese, and an English leaner, and one who want to help you in some way that I can do.
thank you for reading, my computer is now a rather broken, so, I must be hashed way to repair to vist all sites and access all emails too, at present,
so, i'm afraid I can't reccorect my answer in a decent style, for every one.
my answer is a one way to explain.
keep practice, and keep keen to what we are exciting!! we are all traveller in language^^