Issue 1:
It appears that when a type alias to array type which uses an undefined constant for it's size is defined, the compiler crashes. I have only been able to reproduce this with the constants defined in uint modules.

This code

// This line prevents the crash
// use std::usize;

type Array = [usize; usize::MAX];

pub fn main() { }

Causes this ICE

$ rustc --version
rustc 1.4.0-nightly (14b7591ee 2015-08-25)

$ RUST_BACKTRACE=1 rustc test.rs
error: internal compiler error: unexpected panic
note: the compiler unexpectedly panicked. this is a bug.
note: we would appreciate a bug report: https://github.com/rust-lang/rust/blob/master/CONTRIBUTING.md#bug-reports
thread 'rustc' panicked at 'path not fully resolved: PathResolution { base_def: DefPrimTy(TyUint(usize)), last_private: LastMod(AllPublic), depth: 1 }', ../src/librustc/middle/def.rs:80

stack backtrace:
1: 0x112c8e9b0 - sys::backtrace::tracing::imp::write::h3e935b9f3aaf3eeePbs
2: 0x112c969db - panicking::on_panic::h957ddaa69f7f85c8gOw
3: 0x112c5aaa2 - rt::unwind::begin_unwind_inner::hb89bb27d32753510tjw
4: 0x112c5b82d - rt::unwind::begin_unwind_fmt::he8dabdca760d872dziw
5: 0x10fb7f27e - middle::const_eval::eval_const_expr_partial::hf609e26a8506489cQVk
6: 0x10f382980 - astconv::ast_ty_to_ty::h68164822b6891101Fhx
7: 0x10f3f9b21 - collect::type_scheme_of_item::h682b0ea5c5e15cc9d8z
8: 0x10f3f1915 - collect::convert_typed_item::hd9be457a3a816bfbYcA
9: 0x10f3de6a5 - collect::convert_item::h608bb1b0eec4bc39d7y
10: 0x10f3d96a6 - collect::collect_item_types::h044e5c22dac41959Jiy
11: 0x10f425cad - check_crate::h6947ac03da7c9939BAE
12: 0x10f0237b1 - driver::phase_3_run_analysis_passes::closure.20559
13: 0x10f00379a - middle::ty::ctxt<'tcx>::create_and_enter::h16983514113163001088
14: 0x10effee13 - driver::phase_3_run_analysis_passes::h14634090375742016845
15: 0x10efe3424 - driver::compile_input::h6df79a1a00f2ec91Tba
16: 0x10f147e01 - run_compiler::hf8bd4801a975e1fd0bc
17: 0x10f1456e9 - boxed::F.FnBox<A>::call_box::h17883815892091822200
18: 0x10f1450e2 - rt::unwind::try::try_fn::h1123102451065047215
19: 0x112c96598 - __rust_try
20: 0x112c82f60 - rt::unwind::try::inner_try::he6f08bfba5a665ddmfw
21: 0x10f145292 - boxed::F.FnBox<A>::call_box::h10813678079818206125
22: 0x112c9590d - sys::thread::Thread::new::thread_start::h868305d2c1b7d5304Dv
23: 0x7fff95650267 - _pthread_body
24: 0x7fff956501e4 - _pthread_start

Issue 2:
Implementing my own fd_set because, per #26794, I can't find one exported elsewhere. But trying to be clever about the size of the required array causes a panic:

extern crate libc;

pub struct fd_set {
pub __fds_bits: [libc::c_long ; (1024 / usize::BITS)],
}

fn main () {
}

Causes the following output:

error: internal compiler error: unexpected panic
note: the compiler unexpectedly panicked. this is a bug.
note: we would appreciate a bug report: https://github.com/rust-lang/rust/blob/master/CONTRIBUTING.md#bug-reports
thread 'rustc' panicked at 'path not fully resolved: PathResolution { base_def: DefPrimTy(TyUint(usize)), last_private: LastMod(AllPublic), depth: 1 }', ../src/librustc/middle/def.rs:81

stack backtrace:
1: 0x7fc464f645ee - sys::backtrace::write::h04a6ced565b26815Lqs
2: 0x7fc464f6c214 - panicking::on_panic::h521f84b604e22dfel8w
3: 0x7fc464f2f04e - rt::unwind::begin_unwind_inner::hd3dee614a0e1c16cZNw
4: 0x7fc464f2fd7c - rt::unwind::begin_unwind_fmt::ha4ce6704c81423045Mw
5: 0x7fc462f5c059 - middle::const_eval::eval_const_expr_with_substs::h5244545712744191145
6: 0x7fc462f5a532 - middle::const_eval::eval_const_expr_with_substs::h5244545712744191145
7: 0x7fc462f5a8e3 - middle::const_eval::eval_const_expr_with_substs::h5244545712744191145
8: 0x7fc462f0d04b - middle::const_eval::eval_const_expr_partial::h2b23a01d787e9d5efLk
9: 0x7fc464740802 - astconv::ast_ty_to_ty::hb2c49d2cf31c029bYUv
10: 0x7fc4647bcaa3 - iter::Map<I, F>.Iterator::next::h1378750426170396750
11: 0x7fc4647b1ad8 - collect::convert_struct::h6351cd87dbfb23b7u5x
12: 0x7fc4647a3080 - collect::convert_item::h502c0d9543ddcc68AKx
13: 0x7fc46479e467 - collect::collect_item_types::hbd4ad720377bedf8RRw
14: 0x7fc4647ec15b - check_crate::h594ee0148d251222uZC
15: 0x7fc4654c4c69 - driver::phase_3_run_analysis_passes::closure.15783
16: 0x7fc4654c3633 - middle::ty::ctxt<'tcx>::create_and_enter::h349256048753845929
17: 0x7fc4654bea17 - driver::phase_3_run_analysis_passes::h15521018079403107052
18: 0x7fc4654a1266 - driver::compile_input::hbf698b02349f7ce3Tba
19: 0x7fc46557aed3 - run_compiler::hd724b5fef3441688y7b
20: 0x7fc4655788ae - boxed::F.FnBox<A>::call_box::h6609070342514802751
21: 0x7fc4655780f9 - rt::unwind::try::try_fn::h10774555836369096370
22: 0x7fc464fe5d48 - rust_try_inner
23: 0x7fc464fe5d35 - rust_try
24: 0x7fc464f578a7 - rt::unwind::try::inner_try::hb0d7a3eb324339ceSJw
25: 0x7fc46557830b - boxed::F.FnBox<A>::call_box::h18179817771297192954
26: 0x7fc464f6ae71 - sys::thread::Thread::new::thread_start::hf8c7448e27294ed0PTv
27: 0x7fc45eb9c529 - start_thread
28: 0x7fc464bc322c - __clone
29: 0x0 - <unknown>