I'm prefacing this by saying I think Rust is a very well-designed language, and AFAIK the best-designed language that currently exists in its problem space. Nevertheless there are aspects I'd consider design flaws and that fans have been known to dismiss with hand-waving or condescending lectures about type theory. That's a human problem, very much not a problem with the Rust community; in particular I'm quite impressed by how polite and helpful members of the Rust core team are — and not just Steve Klabnik — in every interaction I've seen them in.
1) The syntax is pretty bad; I would put it around the same level as Perl. It's simultaneously ugly, verbose and cryptic. It's especially indefensible given the obvious ML influence on the language. The superficial similarity to C++ syntax is more misleading than helpful and I think actually increases the learning curve.
2) Like the other guy said, the macro system might be technically impressive, but I feel like you shouldn't have to be some kind of Lex/Yacc guru to write or even read a macro definition. Sure, it's fully type-safe, but so is template metaprogramming — compared to which Rust macros somehow manage to be even less readable. There should at least be an easier syntax for simple, C-like macros.
Ok, they're aimed at a different problem space than C macros — they let library authors create sophisticated DSLs — but my impression's the current consensus is "non-idiomatic embedded DSLs considered harmful." Also, Rust is soon to have at least two other macro languages (attributes, and generics with specialization and value parameters), which is a whole lot of cognitive overhead to introduce.
3) All the `.iter()` and `.iter_mut()` is verbose and could easily be inferred from context by both humans and the compiler. If it truly must be explicit — and allowing implicitness as an option doesn't preclude allowing explicitness as well — then introduce new method call operators to go along with the dot operator.
4) I don't think there were compelling enough reasons to abandon the most technically amazing achievement of C++ compilers: zero-cost exceptions. It's the one case I can think of where Rust forces a solution with a runtime cost compared to C++, even in unsafe code. It's also one of the few places where C++ offers higher-level abstractions than Rust. (I'd consider exceptions a higher-level abstraction than Results; of course, higher-level != better).
Arguments based on purity are borderline nonsensical since Rust is not a pure language, the type system isn't aware of side effects, and it's the only case where purity is prioritized over performance. I can respect the idea that errors are either nonserious and so should be handled in the normal control flow of the program, or serious enough to merit a full-blown panic, but I also lean towards the view that it's better to trust the programmer than remove tools from their toolbox.
5) Related to 4, I think Rust should've been designed with C++ binary compatibility as a first-class goal. Yes, this is very difficult, and would require compromising aspects of the language design. But it would be an enormous boon to Rust's adoption rate (and especially the goal of replacing unsafe code in the wild with safe code) if C++ projects could easily be incrementally rewritten in Rust, and it were possible for Rust to directly use C++ libraries and APIs.
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(Yes, this list of issues is not internally consistent; the point is that addressing any of them in isolation would be an improvement).