Starting from emacs -Q:

(defface flycheck-warning
'((((supports :underline (:style wave)))
:underline (:style wave :color "DarkOrange"))
(t
:underline t :inherit warning))
"Flycheck face for warnings."
:package-version '(flycheck . "0.13")
:group 'flycheck-faces)

(let ((ov (make-overlay (point) (point-at-eol)))
(face 'flycheck-warning))
(overlay-put ov 'face face)) ;; C-x C-e this last form to reproduce

After evaluating this elisp, top reports 100% CPU utilization from X.
The face used here is a squiggly underline.  I tried using another face,
isearch-fail face and that overlay was drawn just fine.  I believe the
problem is isolated to this squiggly underline face.  At first I thought
the issue was with flyspell, or flycheck, but these are just examples of
modes that such a squiggly underline.

I am running arch linux, without any desktop environment (I just use Xmonad
and install
whatever else I might want).  The computer is a Dell Precision M4700.

In GNU Emacs 24.3.1 (x86_64-unknown-linux-gnu, GTK+ Version 3.8.2)
 of 2013-08-07 on -mnt-storage-buildroots-staging-x86_64-eric
Windowing system distributor `The X.Org Foundation', version 11.0.11405000
Configured using:
 `configure '--prefix=/usr' '--sysconfdir=/etc' '--libexecdir=/usr/lib'
 '--localstatedir=/var' '--with-x-toolkit=gtk3' '--with-xft'
 'CFLAGS=-march=x86-64 -mtune=generic -O2 -pipe -fstack-protector
 --param=ssp-buffer-size=4'
 'LDFLAGS=-Wl,-O1,--sort-common,--as-needed,-z,relro'
 'CPPFLAGS=-D_FORTIFY_SOURCE=2''

Important settings:
  value of $LC_COLLATE: C
  value of $LC_TIME: en_DK.UTF-8
  value of $LANG: en_US.UTF-8
  locale-coding-system: utf-8-unix
  default enable-multibyte-characters: t

Major mode: Lisp Interaction

Minor modes in effect:
  tooltip-mode: t
  mouse-wheel-mode: t
  tool-bar-mode: t
  menu-bar-mode: t
  file-name-shadow-mode: t
  global-font-lock-mode: t
  font-lock-mode: t
  blink-cursor-mode: t
  auto-composition-mode: t
  auto-encryption-mode: t
  auto-compression-mode: t
  line-number-mode: t
  transient-mark-mode: t

Load-path shadows:
None found.

Features:
(shadow sort gnus-util mail-extr emacsbug message format-spec rfc822 mml
mml-sec mm-decode mm-bodies mm-encode mail-parse rfc2231 mailabbrev
gmm-utils mailheader sendmail rfc2047 rfc2045 ietf-drums mm-util
mail-prsvr mail-utils help-mode easymenu debug time-date tooltip
ediff-hook vc-hooks lisp-float-type mwheel x-win x-dnd tool-bar dnd
fontset image regexp-opt fringe tabulated-list newcomment lisp-mode
register page menu-bar rfn-eshadow timer select scroll-bar mouse
jit-lock font-lock syntax facemenu font-core frame cham georgian
utf-8-lang misc-lang vietnamese tibetan thai tai-viet lao korean
japanese hebrew greek romanian slovak czech european ethiopic indian
cyrillic chinese case-table epa-hook jka-cmpr-hook help simple abbrev
minibuffer loaddefs button faces cus-face macroexp files text-properties
overlay sha1 md5 base64 format env code-pages mule custom widget
hashtable-print-readable backquote make-network-process dbusbind
dynamic-setting system-font-setting font-render-setting move-toolbar gtk
x-toolkit x multi-tty emacs)