Button: specifying only a secondary icon for the button widget locates the icon on the left

The following changes will resolve the issue until an official fix is released:

jquery.ui.button.js:

		_resetButton: function() {
			if (this.type === "input") {
				if (this.options.label) {
					this.element.val(this.options.label);
				}
				return;
			}
			var buttonElement = this.buttonElement,
			buttonText = $("<span></span>")
				.addClass("ui-button-text")
				.html(this.options.label)
				.appendTo(buttonElement.empty())
				.text(),
			icons = this.options.icons,
			multipleIcons = icons.primary && icons.secondary;
			if (icons.primary || icons.secondary) {
				if (!icons.primary)
					buttonElement.addClass("ui-button-text-secondary-icon");
				else
					buttonElement.addClass("ui-button-text-icon" +
						(multipleIcons ? "s" : ""));
				if (icons.primary) {
					buttonElement.prepend("<span class='ui-button-icon-primary ui-icon " + icons.primary + "'></span>");
				}
				if (icons.secondary) {
					buttonElement.append("<span class='ui-button-icon-secondary ui-icon " + icons.secondary + "'></span>");
				}
				if (!this.options.text) {
					buttonElement
					.addClass(multipleIcons ? "ui-button-icons-only" : "ui-button-icon-only")
					.removeClass("ui-button-text-icons ui-button-text-icon ui-button-text-secondary-icon");
					if (!this.hasTitle) {
						buttonElement.attr("title", buttonText);
					}
				}
			} else {
				buttonElement.addClass("ui-button-text-only");
			}
		}

jquery.ui.button.cs:

/* Button
----------------------------------*/

.ui-button { display: inline-block; position: relative; padding: 0; margin-right: .1em; text-decoration: none !important; cursor: pointer; text-align: center; zoom: 1; overflow: visible; } /* the overflow property removes extra width in IE */
.ui-button-icon-only { width: 2.2em; } /* to make room for the icon, a width needs to be set here */
button.ui-button-icon-only { width: 2.4em; } /* button elements seem to need a little more width */
.ui-button-icons-only { width: 3.4em; } 
button.ui-button-icons-only { width: 3.7em; } 

/*button text element */
.ui-button .ui-button-text { display: block; line-height: 1.4;  }
.ui-button-text-only .ui-button-text { padding: .4em 1em; }
.ui-button-icon-only .ui-button-text, .ui-button-icons-only .ui-button-text { padding: .4em; text-indent: -9999999px; }
.ui-button-text-icon .ui-button-text, .ui-button-text-icons .ui-button-text { padding: .4em 1em .4em 2.1em; }
.ui-button-text-secondary-icon .ui-button-text { padding: .4em 2.1em .4em 1em; }
.ui-button-text-icons .ui-button-text { padding-left: 2.1em; padding-right: 2.1em; }
/* no icon support for input elements, provide padding by default */
input.ui-button { padding: .4em 1em; }

/*button icon element(s) */
.ui-button-icon-only .ui-icon, .ui-button-text-icon .ui-icon, .ui-button-text-secondary-icon .ui-icon, .ui-button-text-icons .ui-icon, .ui-button-icons-only .ui-icon { position: absolute; top: 50%; margin-top: -8px; }
.ui-button-icon-only .ui-icon { left: 50%; margin-left: -8px; }
.ui-button-text-icon .ui-button-icon-primary, .ui-button-text-icons .ui-button-icon-primary, .ui-button-icons-only .ui-button-icon-primary { left: .5em; }
.ui-button-text-icons .ui-button-icon-secondary, .ui-button-text-secondary-icon .ui-button-icon-secondary, .ui-button-icons-only .ui-button-icon-secondary { right: .5em; }

/*button sets*/
.ui-buttonset { margin-right: 7px; }
.ui-buttonset .ui-button { margin-left: 0; margin-right: -.3em; }

/* workarounds */
button.ui-button::-moz-focus-inner { border: 0; padding: 0; } /* reset extra padding in Firefox */

Correction:

The jquery.ui.button.cs file I listed previously is incorrect. At some point, I had merged my changes with what must have been an older jquery.ui.button.cs file. The correct file (as of 1.8rc3) is listed below:

jquery.ui.button.cs

/* Button
----------------------------------*/

.ui-button { display: inline-block; position: relative; padding: 0; margin-right: .1em; text-decoration: none !important; cursor: pointer; text-align: center; zoom: 1; overflow: visible; } /* the overflow property removes extra width in IE */
.ui-button-icon-only { width: 2.2em; } /* to make room for the icon, a width needs to be set here */
button.ui-button-icon-only { width: 2.4em; } /* button elements seem to need a little more width */
.ui-button-icons-only { width: 3em; } 
button.ui-button-icons-only { width: 3.2em; } 

/*button text element */
.ui-button .ui-button-text { display: block; line-height: 1.4;  }
.ui-button-text-only .ui-button-text { padding: .4em 1em; }
.ui-button-icon-only .ui-button-text, .ui-button-icons-only .ui-button-text { padding: .4em; text-indent: -9999999px; }
.ui-button-text-icon .ui-button-text, .ui-button-text-icons .ui-button-text { padding: .4em 1em .4em 1.8em; }
.ui-button-text-secondary-icon .ui-button-text { padding: .4em 2.1em .4em 1em; }
.ui-button-text-icons .ui-button-text { padding-right: 1.8em; }
/* no icon support for input elements, provide padding by default */
input.ui-button { padding: .4em 1em; }

/*button icon element(s) */
.ui-button-icon-only .ui-icon, .ui-button-text-icon .ui-icon, .ui-button-text-secondary-icon .ui-icon, .ui-button-text-icons .ui-icon, .ui-button-icons-only .ui-icon { position: absolute; top: 50%; margin-top: -8px; }
.ui-button-icon-only .ui-icon { left: 50%; margin-left: -8px; }
.ui-button-text-icon .ui-icon-primary, .ui-button-text-icons .ui-icon-primary, .ui-button-icons-only .ui-icon-primary { left: .5em; }
.ui-button-text-icons .ui-button-icon-secondary, .ui-button-text-secondary-icon .ui-button-icon-secondary, .ui-button-icons-only .ui-button-icon-secondary { right: .5em; }

/*button sets*/
.ui-button-set { margin-right: 7px; }
.ui-button-set .ui-button { margin-left: 0; margin-right: -.3em; }

/* workarounds */
button.ui-button::-moz-focus-inner { border: 0; padding: 0; } /* reset extra padding in Firefox */

changeset at http://github.com/azatoth/jquery-ui/commit/971c8f5ed40f26d3975a44a96f85ff052f74809d

From http://forum.jquery.com/topic/jquery-ui-button-use-only-secondary-icon

"There's no feature to implement as there's no change to be made in the javascript. As far as the css, the default is for the primary icon to be displayed on the left, secondary on the right. As designed, this can be overridden with css."

"A button with a single icon should have one primary icon and no secondary icon, whether it's displayed on the right or the left."

See also http://forum.jquery.com/topic/a-button-with-an-icon-just-on-the-right

After some more discussion we plan to fix this. Visual test: http://view.jqueryui.com/master/tests/visual/button/button.html

Fixed in 202ddd0