"how to create stuff something"   (some people would pick this because they think that the absence of "in" makes for better keyword optimization)

"how to create stuff in something"   (I pick this because in addition to sounding better to the user it might be clicked more, and being clicked more, in my opinion, is more valuable today than keyword optimization.  Why?  Because google is pretty good at getting the keywords from your article into the title tag but getting people to do what you want them to do takes much more finesse. )

Bah! I swear 80% of my job is convincing site owners that they're thinking is backwards and having to essentially "argue" (for lack of a better word) with them about it.

lol... thanks for the laugh...  Sometimes I feel that exact same way responding to questions here in Q&A.  And sometimes they do ARGUE! and call me a fidiot.

I agree with the subfolder.

I  have always felt that having your brand name in every title tag though-out your website when your URL is your brand name is a waste.

I agree.

The space your brand name takes up could be used for more valuable non-branded keywords. If your brand name is unique,

I agree.

If your brand name is unique, the URL (and content optimized with your brand name) should be enough to have you rank #1 across the board in search results.

If it doesn't you are in some type of trouble with Google... or you really have a weak site.

Though I beleive this I still think it is valuable placing your brand name in the back of your homepage title tag.

Here's what I think... with a few example title tags...

<tltle>MyBigAssCompany:  Golden Widgets - Over 500 Varieties  (these guys think that their ass weighs a ton...  their company name is more important than their message)</tltle>

<tltle>Golden Widgets - Over 500 Varieties | MyBigAssCompany  (OK... at least they are not stinking up the message with their brand name)</tltle>

<tltle>Golden Widgets - Over 500 Varieties  (BAM!   This nails it in my opinion.  Short.  Sweet.  Really, people don't give a damn about MyBigAssCompany... and if they think that the company is really important they are going to see my URL in the SERPs, right below the title)</tltle>

If my company had enormous recognition then I might use the name in the title tag... but I would rather add "free shipping" or some other value proposition than add my brand name to the title.

This is a subject where you are going to get a lot of disagreement and I think that the guy who insists on having HisBigAssCompany on the front end of the title tag will argue a lot louder and longer than I do. 

I am my own client, so I can be as picky as a want, and I take care of the details that I feel are important.

I pay close attention to how the site is responding and rendering when I pretend that I am a visitor.  I pay even more attention when a customer or visitor writes to me with a complaint.   In my opinion, if the site is working great then all is good.    

W3C validation seems to be of jugular importance to W3C evangelists.  They will tell you that you will burn in Hell if you don't achieve it with flying colors.  People who want to sell you their services will point at any fault that can be detected.

Practical people have a different opinion.  I try to be as practical as possible.

Recently it seems Google has started tweaking page titles with one apparent intention: to promote branding.

That article makes a really strong point.   It seems that google does like the brand in the title tag.  They are doing it to a lot of my title tags and I have to say I don't really like it.

I think that this makes the point that google "knows" who is a brand without reading it in their title tag.. but google wants the brand in the title tag badly enough that they are willing to overwrite the carefully crafted marketing message in my title tag to get it there.

In some cases, google might improve the message, but if they are using a one-size-fits all algo they are not going to improve things every time.  If google thinks that I deserve my brand in the title I am flattered, but I'd rather bet on my marketing message than on how their algo will slap a brand name over it in the SERPs.

If anybody has any recommended places to look that would be very helpful as at the moment I am at a loss.

Go look at the SERPs.  Did rankings change?   Did adwords change?  Did google products change?  These are just examples.  You can probably think of more.

Go look at competitors.   Did they change prices?   Did they change shipping?   Are they sold out?  These are just examples.   You can probably think of more.

Go ask the client.   Is manufacturer running ads?   Did manufacturer change MSRP and client didn't?   Was celebrity seen on TV using product?   Did client change HIS price?   Did client change HIS shipping?

There are dozens of other reasons.  And then this could just be one of those "mysteries of life".

Most likely, I think that the answer to this question is going to be found by knowing the business rather than lookin' at tools.

I agree with Russ that the anchors are not going to be indexed separately.... but I believe that those anchors are kickass page optimization that is second only behind the title tag.  More info here.

Unlimited budget?

The first thing that I would do is get a big piece of framed canvas and a bucket of red paint... then paint on that canvas "Don't Blow the Money".  Hang on office wall.

Next get another piece of framed canvas and draw a big line down the left side and a big line along the bottom.  These will be two axes of your chart.  Label the left axis "profitable"... label the bottom axis "linkable".  Hang that on office wall.

Now, every idea that I get for improving the website, write it on a card and pin it on the chart , positioning it along those axes according to its potential profitability and potential linkability.  Work on those ideas that plot with the highest total potential - focus on projects that plot farthest to the right in the early stages then move north.