goodroi - 2:24 pm on Dec 27, 2012 (gmt 0)
If you are worried about a backlink, ask yourself if this backlink will drive good human traffic to your website? If you think you will gain real human traffic that will enjoy your website then it is likely the backlink will help your Google rankings.
If you gain a backlink from a red widget website to your red widget page that is very good. If you gain some backlinks from plastic widget websites to your metal widgets, that is acceptable. If you gain many links from completely off-topic websites to your widget page, that is risky.
If most of your backlinks are from metal widgets and you have few plastic widgets backlinks then you will likely just have better rankings for metal widgets and lower rankings for plastic widgets.
As for large websites that cover many topics, it can be good to gain links from them. If you think the large website will send you good traffic that is interested in your website then it is a good backlink.
Try to get as many backlinks from as many relevant sources as possible. I think you may be too worried about the specific details and are not understanding the general idea of what Google would like to see. Google understands that websites gain a mixture of backlinks - some relevant backlinks and some unrelated backlinks. As long as most of your backlinks are from relevant sites you will be good.