There are several factors possibly at play here (rustc, rustup, rust.vim, syntastic); I chose to report on rust.vim as it is the middleman.

Steps to reproduce

1. Install both rust.vim and syntastic. For full disclosure: from a clean vim, I installed pathogen, cloned the plugin repos into .vim/patho, and used this .vimrc

   execute pathogen#infect('patho/{}')
   set statusline+=%#warningmsg#
   set statusline+=%{SyntasticStatuslineFlag()}
   set statusline+=%*
   

2. Make two new crates, one on nightly

   cargo new --bin test-nightly && (cd test-nightly && rustup override set nightly)
   cargo new --bin test-stable
   

3. For each one, do the following:

    $ cd <test dir name>
    $ vim src/main.rs

Verify that all lights are green:

    :SyntasticInfo
    Syntastic version: 3.7.0-180 (Vim 704, Linux)
    Info for filetype: rust
    Global mode: active
    Filetype rust is active
    The current file will be checked automatically
    Available checker: rustc
    Currently enabled checker: rustc

Insert a deliberate error (unpared parenthesis) and write the file.

    O(<Esc>:w<Enter>

What occurs

In test-stable: After the file is written, syntastic will flag errors in the gutter and statusline.
In test-nightly: After the file is written, nothing happens.

Versions installed

uname -a: Linux lampam-ThinkPad-T430 4.4.0-31-generic #50-Ubuntu SMP Wed Jul 13 00:07:12 UTC 2016 x86_64 x86_64 x86_64 GNU/Linux
rustup: rustup 0.5.0 (4be1012 2016-07-30)
rust.vim: (git hash) 7304385
syntastic: (git hash) aa2a09110956e46652a9cb247ec24a57797066fd
vim: VIM - Vi IMproved 7.4 (2013 Aug 10, compiled Jun 16 2016 10:50:38)

Versions of rustc tested: (OK means syntastic highlights the error)
OK: rustc 1.10.0 (cfcb716cf 2016-07-03)
OK: rustc 1.11.0-beta.3 (052e32bd9 2016-08-08)
FAIL: rustc 1.12.0-nightly (0ef24eed2 2016-08-10)
FAIL: rustc 1.12.0-nightly (8787a1233 2016-08-11)