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Don't need a separate computer just use a proxy service when logging in So your not using the same IP.

Face Palm - Probably want to start all over your making to much work for the search engines and they don't like it.

Yes I think this could give an algo penalty to the clients. You never know how the big G will perceive it. But better to be safe and keep everything separated.

Good find on the white board video that's got a ton of useful info.

Looks like your trying to cover a particular key term. Building a bunch of sites and trying to get them all ranked on P1 so you saturate the market. It's been done way to much. Google is very smart in detecting these things and it will effect the rankings. The fact you have them all linked in 1 login is a big Neon Billboard not a small red flag. They have already logged your email and associated everything to those domains.  These sites will now just be valid burn sites you can dump later.

The duplicate content issue you can easily solve by installing Yoast SEO plugin and noindexing the tag pages (you can also noindex categories, archives etc if you need).

Here is a great guide to stetting up the plugin properly and eliminating those page duplication errors http://moz.com/blog/setup-wordpress-for-seo-success

Hope this helps!

What CMS are you using?  Could be a problem with a plugin or code.

Are they same or similar products or subject matter?  Do you have any interlinking of the sites?

Magento is great and has a plugin perfect for this so you can add that in. http://www.magentocommerce.com/magento-connect/product-video-with-swatch.html

There are so many better ways to do this.  What framework are you using?  Woo Comm has this feature http://wordpress.org/plugins/woocommerce-video-product-tab/

Well if you think the brand exposure TSC has that catapults them to top rankings.  If you a small retailer selling Horse Stall Mats with zero brand it will be an uphill battle.  However I have found the amount of on page content plays a minimal role to the overall ranking factor.  The biggest factors would be to have great branded links that pertain to your business, Social Media Presence with high engagement, and useful evergreen content on your site for people.

It looks like you have decent rankings for that keyterm. With out going to involved it looks like a little push from links to that page and work on your social media engagement since that's really lacking.

Use Firefox and access it.  I had this same issue a few months back and it was something to do with a glitch in the system and an update to FF and IE.

Once logged in try going to this link  http://analytics.moz.com/manage-campaigns it's a work around for the time being.

And make sure to Contact support help@moz.com and relay your issues.

Yep there pulling authors with little G+ juice.

Shawn is correct. Domian tools will give you a great history plus info on the current owners other domains.

How do you know they are earning good money for those terms?

Footer links should not be overused in fact limit them to only a couple. You want to design and create experiences for the user don't focus so much on google and ranking.  If it is of value to have that link for a user then it will not hurt you.  Rand has a great article on this http://moz.com/blog/footer-link-optimization-for-search-engines-user-experience

Your going to have to disavow tool those links and you might want to take a big chunk of your links out and start over. Like Matt Cutts said use it like a Machete not like a Scalpel.

Yet another bit to read http://searchengineland.com/googles-matt-cutts-link-spamming-google-for-a-specific-time-period-then-mass-disavow-those-links-179445

That would be achieved with content marketing.  Better known as "Guest Blog Posting" Your gonna have a lot more reading to do.  The great part is knowledge is power when it comes to marketing.

If you have not read this yet MOZ SEO GUIDE do so as it will get you on the right path. Heck even if you have read it do it again for a nice refresher as this get updated.

Read These on Guest Blog Post
http://moz.com/blog/12-scalable-link-building-tactics http://moz.com/blog/the-ultimate-guide-to-advanced-guest-blogging

Pintrest will help to deliver your brand or product to consumers eyes and generate more traffic.  But there link worth is low until you build a large following.

Are these real people?  G+ has a facial recognition and will remove stock photos etc.

This has been gone over several times. Below are some great links to help you with that.

http://moz.com/blog/40-important-local-search-questions-answered

http://www.localseoguide.com/seo-for-businesses-with-multiple-locations-in-the-same-city/

http://www.clickz.com/clickz/column/2283736/local-seo-strategy-for-the-multilocation-marketer

James, Are you running FB ads? Do a quick audit and make sure they are not a bunch of junk likes.  I have seen this from competitors trying to lower Edgerank scores so your ads become unseen by others on FB.

Here is a good read http://blog.nakedlime.com/2012/09/fake-facebook-likes-and-the-trouble-they-cause/

Nope No value. Another SMB scam tactic...

No that would be against G+ TOS. You would need to use the rel=publisher tag instead and link to the business G+ page.

It will help drive some traffic though you need to have high quality articles that are informative and provides value to the reader.  The links are no follow but who cares your using it to gain traffic based on the article. Quit trying to game google and build useful content for the internet.

Try building some followers to FB fan page, Get Likes and make sure you have a branded url for it. You should see it pick up after that.

This is an issue there fixing you can keep track of known problems here http://health.moz.com/ if you have futher issues you can also email help@moz.com

Yep this has already been posted. But you can read the post here.
http://moz.com/community/q/google-analytics-keeps-poping-up-that-i-need-to-re-authorize#reply_205099

No this would not boost the DA for your page.  The link itself would help increase the overall DA but not the CTR on the link. So if you thinking about buying traffic through that link don't waste your money it will only spike server traffic. Best thing is to focus on QUALITY everything from your links, social media, and the major one Useful content. There is no overnight trick to boost your DA and it takes time. But creating value for the end user and not google you will see a rise in Conversions and DA.
You can read more in depth here about the factors that go into play with DA
http://www.searchenginejournal.com/care-domain-authority/

Also read the Basics http://moz.com/beginners-guide-to-seo

Usually fixed within a few days if it's a known error.  Email them about this at help@moz.com and they can assist you further.

Yep I agree 99% with you. Bugs are a normal thing and since the new MOZ came out of beta it has been plagued with them.  There are several other great tools out there that do the same thing and maybe better. One I love is Raven Tools

Certainly! Here is a great read on content length. But again Quality will be the biggest factor.

http://www.quicksprout.com/2012/12/20/the-science-behind-long-copy-how-more-content-increases-rankings-and-conversions/

Still around 700+ There is really not a formula as pages with 300 words rank very well.

This is an issue there fixing you can keep track of known problems here http://health.moz.com/

Are you doing any type of PPC? That can cause some issues with there content network ads.