Mutability - everything you "own" on synthetix is fully controlled by the devs.
They admit to it in the whitepaper (page 13 (16 in pdf))":

"It would be a simple matter to implement a democratic remedy, weighted by havven balance, by which havven holders can freeze or confiscate the balance of any contract that wraps assets.
Those havven holders are incentivised not to abuse this system for the same reason that bitcoin mining pools do not form cartels to double-spend: because abuse of this power would undermine the value of the system, and thus devalue their own holdings. The credible threat of such a system existing is enough to discourage token wrappers from being used, even if they are written, since any user who does so risks losing their entire wrapped balance."

The names changed: havven is now SNX and nomins now mean any "synth". SNX holders gain fees from synth movement, but those fees can be escaped by wrapping synths in a contract (like WETH). Their solution? Threaten confiscation of wrapped synths.
Is it a credible threat on the contract side? Yes: sUSD contract. It's a contract proxy.
The target contract is set by:

function setTarget(Proxyable _target)
        external
        onlyOwner
    {
        target = _target;
        emit TargetUpdated(_target);
    }

the owner, at the moment, is 0xb0A23F40De7F776A4f20153e8995eD3E7D7c8487 - a normal ethereum address.
The owner of that address can do literally everything - lock, confiscate, arbitrarily change balances, or just kill the system by changing the target contract address.

This alone should be enough to stay away.

Problems with the peg mechanism.
I started writing an analysis, but found a good one already existing here.
In short, the backing system only works as long as fees grow. The moment the growth stops, it collapses. It's not backed by ETH (like DAI currently), not even SNX, but only by a future discounted value of paid fees.
Why does the system sort-of work currently? Because of manual (ie. effectively bank account-backed) peg, admitted in the whitepaper as an early stage: "Given that it’s necessary to encourage liquidity, but not all the mechanisms outlined in this paper will be operating yet, issuance will be by the foundation itself, and potentially other white-listed addresses it trusts. In this way, the stability of the token is maintained by direct market intervention by the foundation." (p24/27)
As long as they continue to do that, the synths are probably going to work, but in a fully centralized manner.

The centralization and full control over funds creates a legal issue. Synthetix is de facto a centralized CFD platform with no kyc/aml at all. It's virtually certain they are breaking securities and money transmitter laws in most countries in the world, especially as they plan to introduce stock CFDs. Very similar to 1Broker which was raided in 2018.