Update: Actually it looks broken in Firefox too.

I was running JIRA 6.0.4 in our development instance, and noticed that 6.0.6 was released fixing IE8 issues.

After the upgrade IE 8 + 10 on multiple machines, has rendering issues which were not present in 6.0.4

It looks like this is down to the 'Assigned to me' gadget.

The standard dashboard looks fine, as it doesn't have the 'Assigned to me gadget', however adding it re-creates the problem.

IE10:

My 'Assigned to me' box appears be to a restricted size, unable to edit (save button missing).

IE8 Debug:
Webpage error details

User Agent: Mozilla/4.0 (compatible; MSIE 8.0; Windows NT 6.1; WOW64; Trident/4.0; SLCC2; .NET CLR 2.0.50727; .NET CLR 3.5.30729; .NET CLR 3.0.30729; Media Center PC 6.0; InfoPath.2; .NET4.0C)
Timestamp: Wed, 7 Aug 2013 09:44:09 UTC

Message: 'AJS' is undefined
Line: 2
Char: 1
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:util-lite/jira.webresources:util-lite.js

Message: 'AJS' is undefined
Line: 2
Char: 1
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:util-lite/jira.webresources:util-lite.js

Message: 'AJS' is undefined
Line: 2
Char: 1
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:content-retrievers/jira.webresources:content-retrievers.js

Message: 'AJS' is undefined
Line: 2
Char: 1
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:content-retrievers/jira.webresources:content-retrievers.js

Message: 'AJS' is undefined
Line: 2
Char: 1
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:inline-layer/jira.webresources:inline-layer.js

Message: 'AJS' is undefined
Line: 2
Char: 1
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:inline-layer/jira.webresources:inline-layer.js

Message: 'AJS' is undefined
Line: 2
Char: 1
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:list/jira.webresources:list.js

Message: 'AJS' is undefined
Line: 2
Char: 1
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:list/jira.webresources:list.js

Message: 'AJS' is undefined
Line: 2
Char: 1
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:dropdown/jira.webresources:dropdown.js

Message: 'AJS' is undefined
Line: 2
Char: 1
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:dropdown/jira.webresources:dropdown.js

Message: 'AJS' is undefined
Line: 2
Char: 1
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:issue-table/jira.webresources:issue-table.js

Message: 'AJS' is undefined
Line: 2
Char: 1
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:issue-table/jira.webresources:issue-table.js

Message: 'JIRA' is null or not an object
Line: 2
Char: 14
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:util/jira.webresources:util.js

Message: 'JIRA' is null or not an object
Line: 2
Char: 1
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:autocomplete/jira.webresources:autocomplete.js

Message: 'JIRA' is null or not an object
Line: 2
Char: 14
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:util/jira.webresources:util.js

Message: 'JIRA' is null or not an object
Line: 2
Char: 1
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/1.0/_/download/batch/jira.webresources:autocomplete/jira.webresources:autocomplete.js

Message: Object doesn't support this property or method
Line: 4
Char: 9
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/6.0.6/_/download/batch/com.atlassian.jira.gadgets:core-gadget-resources/com.atlassian.jira.gadgets:core-gadget-resources.js

Message: Object doesn't support this property or method
Line: 4
Char: 9
Code: 0
URI: http://jira-dev.snellwilcox.local/s/en_UK5ygja8-1988229788/6105/5/6.0.6/_/download/batch/com.atlassian.jira.gadgets:core-gadget-resources/com.atlassian.jira.gadgets:core-gadget-resources.js

Message: 'AJS.Dropdown' is null or not an object
Line: 341
Char: 29
Code: 0
URI: http://jira-dev.snellwilcox.local/plugins/servlet/gadgets/ifr?container=atlassian&mid=14362&country=UK&lang=en&view=default&view-params=%7B%22writable%22%3A%22false%22%7D&st=atlassian%3ALotGIe2g%2BtMKIMIhZou4u8YDh3H6GdX6qH42bk8QM%2B1WeZkhMjsEXMcy8OlxScGEvL99z4KUhgSFF2o9fOvBfpykuTDIxZPRvJroVB5whWoyN1T6hzDTlsdKT7jvuhq2NEZkrfpjWeNXmYhkMHtIyU82McXxGAEvtA71AmeHKTqXHrNyoAINn6KxJxMADFr0G2jCJqMvNf1lBJLvAFiSXUp3l7cFRmzRfo0ZjiRcj%2F5TZw3dXGHZu%2BIv9Ph1ZspGJNZ3tWBjvgnU6l694CaNCJaYwVstHQdZY6qjVl8DrVahbs%2FFQbfP0BrvPT1MMtYMO4iDBw%3D%3D&up_num=37&up_isConfigured=true&up_columnNames=--Default--&up_sortColumn=&up_refresh=15&url=http%3A%2F%2Fjira-dev.snellwilcox.local%2Frest%2Fgadgets%2F1.0%2Fg%2Fcom.atlassian.jira.gadgets%3Aassigned-to-me-gadget%2Fgadgets%2Fassigned-to-me-gadget.xml&libs=auth-refresh