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I have noticed that some of my title tags have been altered (by Google?) on the SERP. I am only showing the keywords on some listings, not the full title tags that I wrote, this is happening to our competitors as well. Any idea what is going on, one of my clients is looking for answers! Thanks

A client of mine wants to look into new areas of link building after convincing them that their current link building strategies (purchasing multiple links from god knows where) was not working well for them. Essentially I felt they were spinning their wheels. Now, we are looking into content related blogs to get some honest links for their site. They sell sports equipment and we are looking at sports blogs to get links/partnerships. Most of these blogs want sponsorship fees or advertising fees. From an ethical standpoint I understand buying links is not the best idea. But because these are blogs that earn traffic, have relevant content, and can be helpful for the advertisement aspect to link to people who might be interested in their products as well. There shouldn't be a problem in acquiring a few of these links if the budget allows for it, correct? Also are blogs a good source to acquire links from?

I have a client who has a blog with a side bar on each page, in the sidebar there are various links to the site, as well as links to some of his partner sites. I was looking at the recently updated open site explorer, and noticing that their domain authority is way down, a good amount below their competitors as well. The total links compared  to the linking root domains is ~3000 to 200. So my question is 1. How can I gain on the domain authority front? (more diverse links?) And if so, 2. Should I no-follow the links on their blog so they don't have hundreds of pages with the same links (most internal) on there site Thanks,
Nick