Taking into account what your're saying here, one would then assume that inbound backlinks could never cause a penalty too - since competitors could do that intentionally as well? If Matt Cutts was reading this, he'd probably be all over you...

Since there are mixed opinions here, probably my short 'yes' didn't help, so here is my opinion, in little more details.

If 301s could ONLY pass juice but not penalty, wouldn't everyone try to get as many 301s as possible - ie. acquire dozens of sites, pay other webmasters to do 301s, etc? Think about it. In effect, the 301 would act as a 'paid' backlink except only more powerful and it would be much easier for everyone (with $) to game rankings.

If you still don't believe 301s can potentially pass a penalty, you can refer to this thread:
http://www.webmasterworld.com/google/4323639.htm

In short - Yes it can

Is your blog hosted on a subdomain?

Personally I have noticed that Panda is sitewide but the subdomains might remain unaffected. In our case, our ecommerce site with 6,000+ pages got affected but the blog (subdomain) actually increased in traffic due to better content, more social signals and other factors.

Absolutely no penalty for multiple links to a single page!

I usually just use Xenu's link sleuth (if you thousands of pages) to list out all the URLs you have and I would then manually check them, but I haven't come across an automated tool yet. If anyone knows any, I'd love to know as well.

Really interesting that you ask this as I have just recently been researching on this exact same thing. A website where we had 4 H1 tags on homepage (not a good thing!) needed to change - to keep it to just 1. I did not want to introduce new keyword phrase and I struggled to find an existing keyword/title phrase that I could wrap the H1 with. For a sometime I was considering making the logo as H1 as the logo images ALT  had the websites main keywords in it but from research and non-scientific test on a dummy site, I found that its not very affective at all.

To some extent, the effect is like an image backlink - Google does not greatly value the ALT of the image that is linking to you, as it would, had the backlink been from a text link with anchor text.

No issues at all.. have been using them for years