I see a link to http://www.odin-groep.nl/Home/ctl/OverOdin/OverOdin/HeutinkICT.aspx from http://www.odin-groep.nl/Home/ctl/OverOdin/ReindersICT.aspx.

It's the bottom left block which causes this link. This way you will get a big nesting effect.

Which URL(s) is/are causing problems?

You don't necessarily have to remove the link. As long as you can verify that it directs to the right page.

But curious to see what caused the problem

Are you somehow linking to www.website.com/dogs/dog.html from the page itself? There could be something wrong with that link.
I made a small mistake not so long ago with a redirection plugin. I told it to go to domain.com. This plugin was looking at the base + what i told it to. So it went to: domain.com/domain.com. Perhaps you made a similar mistake.

Maybe you can send me the URL and i can take a look at it?

That shouldn't hurt your site. I rebuild an e-commerce site which had 50.000 redirects in place at the moment i was working on it. Of course it adds a little bit of load to the server but it's not really noticable. This way you will keep the value of the old links.

Thomas Hall is right about the soft 404 pages being generally more acceptable. If you care more about the user experience then about the value from your old links then you could build a dynamic 404 page.

This page should tell the visitor that the product no longer exist and should give them a couple of products which are similar of relevant to the product they were searching for. This way you will improve the user experience with a soft 404.

Just to be clear, you don't have to set a redirect to the home page. You could also do it to the category pages or to popular products. It's very difficult to say since i don't know which branch your in. Who your target group is and what they are interested in.

The 301 redirect would be a better option.

I will try to explain why this is better than a 404 page.

1. If people posted a link to the product PageRank to your website.(This is one of the ranking factors in Google) If the page doesn't exist anymore and brings up the 404 page it will lose the value from all the links to that particular product. If you use a 301 redirect to send visitors to a relevant product or to the homepage then the value from those links will have effect on the page where you send them to.

2. Nobody likes a 404 page. There are very cool things you can do with a 404 page so that they are still helpful to the visitor such as most popular pages, a search function and even jokes. But in the end nobody would have clicked on the link or typed in the url to your website and think: Now i want to see his 404 page.

I hope i answered your question. Let me know if anything was unclear.

It has a lot to do with the kind of website that you have.

In general you want to get a lot of links to the pages that you want to get found on. (blog posts, product pages etcetera)
But in general the homepage gets the most links because when people see your website and they like it the homepage is the most logical URL to link to.

Strengthening the home page will be helpful to your site because the homepage should be your content hub. You can find more information about content hubs, website architecture and a lot more here: http://moz.com/blog/how-to-rank

Hope i answered your question
Let me know if you have any other questions or if i was unclear about something.

Very good one Takeshi. Didn't think about whether the site in question had similar products like these. You are also right about the user reviews.

User reviews are a great way of getting unique content on a page. If you implement user reviews and ratings make sure you mark them up with structured data such as HTML5 Microdata. This way it can appear in the rich snippet. This page explains a lot about it: http://support.google.com/webmasters/bin/answer.py?hl=en&answer=173379&topic=1088474&ctx=topic

4000 products is indeed a hell of job to tackle if you want to write an original description for every single one of them. It is recommended to do this since it will improve the site.

I agree with Doug that you should start on the products which sell the most because you want to get found better on these products. I would start doing a given amount of products each day and keep good track of which products you did and which you didn't change.

Furthermore what i think is the most important thing is the title tags and description tags of those 4000 pages. Are they well optimized? Even if the pages are ranking well at this moment the title and description tags are the only way you can convince the visitor to click on your link in the search results and therefore they should be compelling and descriptive.

Very descriptive answer. Love that you describe your entire experiment.
Thank you for this extra bit of information.

A 303 won't send 'link juice' that means that all the value you website gets on mywebsite.com won't be send to mywebsite.com/fr/. You should use a 301 instead.

I've worked with some e-commerce sites before. I'll try and explain the way i handled it.

1. Know the opportunities and limitations of your CMS (Content Management System). I've worked with Magento and i did a lot of things by myself which were done automaticly by Magento. Such as creating XML sitemaps. Knowing what your CMS does for you helps you focus on the weak points of the CMS.

2. On page optimisation: An E-commerce site wants to get found on it's products in most cases. Are your product pages optimized? Make sure that all your product pages have a really good title and description. Not only for SEO purposed. Of course having your important keywords in there helps but make sure people would click on it too. Find someone from your target group and ask them about the quality of your titles / description. Would they click on it? If no, then why not. Use their feedback to improve them even more. Product descriptions should be really good too. This webshop http://www.vat19.com/ really knows how to create product pages which are aimed at their target group and contain a lot of content. The images and video's are rich media which are relevant for the target group and Google loves this.

3. Social: There are so many possibilities for E-commerce websites on the social platforms. Make sure you have a Facebook page, twitter account, Google+ account and Pinterest account. The buttons should be implemented on at least the product pages as well. Facebook and twitter allow you to reach your target group and get more exposure to other people. It is now even possible to include webshop functionality on Facebook pages. Google+ will soon get this too if i'm not mistaking. I mean they have Google shopping and they are making Google+ the center of all Google products with an added social layer. Pinterest allows you to pin all your products and recently they added the option of adding prices and stock to your pins.

4. Link building: As Takeshi said before this is an excellant list of link building techniques: http://pointblankseo.com/link-building-strategies. Make sure you have content that people want to link to. Some e-commerce solutions offer a blog next to the webshop and i know that there is a Magento plugin for making a connection to Wordpress. A blog is something to get a better connection to your customers and is great link bait by itself. If you do other things such as product review video's or so this is also an excellant place to gather feedback from customers.

I hope i helped you somehow and if you want more advice or if anything was unclear please let me know.

Good luck