You see, the function of the H2 and H3 tags doesn’t exist on the home page (category and page title, respectively). So if I choose to stay structured with my headings, then I have to restyle H2 and H3 to look appropriate on the home page. However, I could skip straight to H4, which is the visual style I need, but things will then be out of order.

The former is semantically correct. The latter would seem to be easier to maintain.

1- First of all, it doesn”t seem like there is a consensus on wether or not to use multiple H1 tags, or any at all.

Pages should only have one main heading, H1, which is the main title of the page and should be positioned at the start of unique page content.

2- In the example you mentioned, you set an H before the form field.
Search
(…inputs…)

Upon the accessible headings:
Headings should not be coded around form labels i.e. the text label “Search” that comes before an input field.

3- Here, the order is h1-h4-h2-h2-h3.
Heading levels can”t be skipped i.e. you can”t jump from H1 to H3.

Reference: http://www.rnib.org.uk/wacblog/headings/quick-tips-for-accessible-headings/

I am totally uncomfortable with skipping header tags (i.e. h1, h3, h4, . . .), but I think Eric’s reasoning is sound.

These issues are often mitigated by good pre-planning. Therein lies most confusion. Amateur designers dive into their work without thinking through the entire project. Then, when their headers, paragraphs, titles, etc. don’t play nicely together, they struggle to fix a design that wasn’t right to begin with!

Alternatively if you really wanted the search to be h4 it could be put at the end of the document in the correct nesting level and then moved up to the top with css? This would be the most semantically correct way to go in my opinion.

Hear, hear to hierarchical, non-skipping headings.

My feelings are that accessible markup should take priority over the (x)html markup of your choice.

My weapon of choice when performing accessibility checks is the http://bobby.watchfire.com service.

To achieve a grade 2 (out of 3) level of accessibility headings need to be sequential (h1 is followed by h2, and not h3), which agrees with the W3C.

The reasons for this seem to be different, however. As already mentioned in other comments W3C specifies that headings should be ordered according to importance. Accessibility standards generally state that headings are for defining the flow of a document.

The styling of the headings is irrelevant. It would be valid to assign values of importance to each header:

	h1.importance1 {
	    font-size: 2em;
	}

	h1.importance2 {
	    font-size: 1.8em;
	}

etc.

This level of complexity is something I am not prepared to even contemplate using, and the assigning of classes to header tags is a step back towards merging design and content.

In this situation possibly W3C is wrong in its definition of headings. Accessible design should come first, and this means that the flow of documents should make sense without additional styling.

Since some users skim through a document by navigating its headings, it is important to use them appropriately to convey document structure. Users should order heading elements properly. For example, in HTML, h2 elements should follow h1 elements, h3 elements should follow h2 elements, etc. Content developers should not “skip” levels (e.g., h1 directly to h3).

The confusion over whether or not to skip heading levels perhaps is rooted in our misunderstanding of the basic aims of HTML which I feel should be to only show hierarchy rather than to try to make HTML also show “importance”.

Here are some further thoughts with a diagram:

http://www.ryznardesign.com/web_coding/elements/2004/headings/headings.html