To answer your question: No, it's not okay. Duplicate content is to be avoided. Ask your programmer to do a 301 redirect one of these pages to another, that automatically redirects users and the GoogleBot, or at least add an canonical url meta tag which defines which page is the "original" or "canonical" version for the content.

See more at Google Support.

As to why it is happening. Difficult to be precise but would venture that one of the URL-s might be a category "page" that gets created automatically, with an url thanks to your page's category structure and the other a real editable "page".

Google states on their support page:

_If we’ve detected that a particular result has [...] issues with its title, we may try to generate an improved title from anchors, on-page text, or other sources. However, sometimes even pages with well-formulated, concise, descriptive titles will end up with different titles in our search results to better indicate their relevance to the query. _

There’s a simple reason for this: the title tag as specified by a webmaster is limited to being static, fixed regardless of the query. Once we know the user’s query, we can often find alternative text from a page that better explains why that result is relevant. Using this alternative text as a title helps the user, and it also can help your site. Users are scanning for their query terms or other signs of relevance in the results, and a title that is tailored for the query can increase the chances that they will click through.

What to do? Here's the answer:

• make your title mean something as a sentence or a phrase. List of keywords is not descriptive of what is on the page. Therefore Google will not use that. There are exceptions for e-commerce or product sites but that is the rule.
• If you want to highlight a certain keyword — simply place that at the start of the said phrase in the title.
• try to think as an user searching for your page when composing the above mentioned phrase. What do they desire?

For more, please see my previous answer at http://moz.com/community/q/title-tag-issue-2

Hi, here're the 3 steps that should work easily:

1. Add the canonical URL-s as you already know how. Wait for the new domain to rank. But don't stop there.
2. After you've seen new domain rising place robots.txt and no-index meta tags on the old site instructing Google not to index it.
3. Use Google Webmaster Tools to request Site Removal for the old site: under Google index -> Remove URL-s place the full domain of your old site. You should see that instead of a "page removal" you will be asked to confirm a "site removal". More instructions here from Google.

Your suspicion seem to be warranted since Moz reports that for the July 2013 Panda Update: "The implication was that this was algorithmic and may have "softened" some previous Panda penalties". But on the other hand they state there were ranking fluctuations weeks prior to that, which they called "massive".

So what happened the weeks prior? This article by Moz's own Dr. Peter J Meyers provides a glue but nothing substantial: http://moz.com/blog/googles-multi-week-algorithm-update — it suggests that you may have been of the PMD's (partial match domains) or EMD's (exact match domains) that did not recover from that update. Curiously he also mentions the possibility that these might have been directly targeted.

Possibilities:

1. You were directly targeted by Google. In which case your mission is to convince Google that you are now a good citizen. Better internal linking is a stronger sign of becoming non-spammy than going on an external link campaign.
2. You were caught in a wider net of EMD's and PMD's that Google calculated to be too spammy and got a temporarily hammered. But adding the 301-s then took away your chance to recover via good internal linking that otherwise may have happened naturally ("blue widget" suggests you may run an e-commerce site). These two have identical results.

What to do:

1. Remove 301, keep the canonical URL-s. As Thomas suggested.
2. Add or renew internal links thoughtfully (couple of in-context links and related products, top sellers per page) and overview your breadcrumbs (if not already there).
3. Add semantic SEO product (or whatever is relevant to you) mark-up, more unique images — everything you consider appropriate to signal to Google that you are not "spammy" anymore.

Just remember, you may no longer rely on your domain name to rank.

You should aim to be closer to 1, rather than 50.

Why? Because the numbers indicate the ranking or placement of your page on the search results page(s) (SERP). Number 1 indicates a page on top of the search results page (at least for the organic search).

You should aim to be closer to 1, rather than 50.

Why? Because the numbers indicate the ranking or placement of your page on the search results page(s) (SERP). Number 1 indicates a page on top of the search results page (at least for the organic search).

Google states on their support page:

_If we’ve detected that a particular result has [...] issues with its title, we may try to generate an improved title from anchors, on-page text, or other sources. However, sometimes even pages with well-formulated, concise, descriptive titles will end up with different titles in our search results to better indicate their relevance to the query. _

There’s a simple reason for this: the title tag as specified by a webmaster is limited to being static, fixed regardless of the query. Once we know the user’s query, we can often find alternative text from a page that better explains why that result is relevant. Using this alternative text as a title helps the user, and it also can help your site. Users are scanning for their query terms or other signs of relevance in the results, and a title that is tailored for the query can increase the chances that they will click through.

What to do? Here's the answer:

• make your title mean something as a sentence or a phrase. List of keywords is not descriptive of what is on the page. Therefore Google will not use that. There are exceptions for e-commerce or product sites but that is the rule.
• If you want to highlight a certain keyword — simply place that at the start of the said phrase in the title.
• try to think as an user searching for your page when composing the above mentioned phrase. What do they desire?

For more, please see my previous answer at http://moz.com/community/q/title-tag-issue-2

To answer your question: No, it's not okay. Duplicate content is to be avoided. Ask your programmer to do a 301 redirect one of these pages to another, that automatically redirects users and the GoogleBot, or at least add an canonical url meta tag which defines which page is the "original" or "canonical" version for the content.

See more at Google Support.

As to why it is happening. Difficult to be precise but would venture that one of the URL-s might be a category "page" that gets created automatically, with an url thanks to your page's category structure and the other a real editable "page".