First of all, the most important thing is if the optimise the page that's ranking for that keyword(title, h1 ,descr,etc)
And then the most important thing I do is analysing their backlinks and looking at their anchor text. In my opinion this is the most crucial thing to look at when analysing keyword competition.
I have found a keyword about a week ago, and the first website ranking had a little over 5000 backlinks and a domain age of 7 years. The searches for that term is quite high, so I thought I would do a little more research.And guess what....not even 1 of their backlinks had the anchor text of the keyword I was analysing.
I have quickly bought a emd and done some social bookmarking to index my site fast, and guess what, I am number 1.
I truly beleive that people stress to much about the number of competing pages, intitle search, inurl search and all the rest. All that really matters is emd, domain age, the top 10 ranking page, on-page seo, backlinks quality and the anchor text of the backlinks. The backlinks number is not always relevant. As they can have loads of pr0 backlinks ...just create a few high pr backlinks and you will see results.
Please feel free to add anything!