Rasputin - 1:20 am on Jan 1, 2013 (gmt 0)

The absence of H1 in itself is not a problem IMO - many category pages and home pages do not have an H1, on lots of sites (including my own main site which has not suffered as a result)
The presence of a material % of pages that are 'noindex' can perhaps be a problem though, in certain circumstances and if this represents a significant % of the sites pages and the pages are of low quality.