Are there any bitcoin network flaws that can be exploited to gain money without losing other people's money in the process.
Yes, but probably you can't get much money out of them.
For instance Selfish mining is one (if you interpret that the remaining miners are not "loosing money", but just earning less money).
Certain design failures in the Bitcoin mining algorithm (double SHA-256 of the header) also allow non-obvious speedups that miners may be exploiting or may exploit in the future to obtain a small advantage. All commercial Bitcoin ASIC designs are confidential.
And some critical things don't leak so easily. As a comparison, Pieter Wuille held information about a critical bug in Bitcoin for a year until it was finally solved.
I think that the incentive to exploit weaknesses is low for many different reasons: low monetary gain, high initial cost to setup the exploit, high economic penalty if exploit discovered, personal reputation at stake, legal concerns, etc.
Bitcoin is fantastic for a lot of reasons, but it is not perfect.
