We have our main catalog site, a industry trade publication, and several product specific mini-sites. Are there any drawbacks to this kind of network for building traffic?

You have multiple business websites serving the same audience, each with their own theme and visitor value. I find one of the biggest drawbacks to build such a network of sites is maintenance. But it does have value.

First, as long as each site focuses on a specific subset of visitors and doesn't participate in any silly link schemes, then you are likely to make search engines happy. This is a useful part of the model I use for my publishing effort.

Disclosure: Justin Hitt is the owner of the JWH Consolidated Network, the Worlds Largest Network for Sales and Marketing Professionals in Business-to-Business Industrial and High-Tech Organizations with more than 72 active websites.

To get around the service issues, I've seen businesses team up with publications and other resources serving the same audience. This network of sites provides more value, plus editorial independence customers are seeking.
This is what I call collaborative networks (which includes joint venture efforts between sites.) Some of the blogs are starting to talk about this, but it has been around forever. You don't need to be an Internet.com sized publisher either.
Just make sure all your network content is unique and exclusive, so many marketers get lazy and want to recycle old content that has little value. You'll also need to manage your partners to make sure they don't get lazy (i.e. leeching all your hard earned traffic, while sending you very little value.)
This type of collaborative arrangement can also pool advertising dollars. As you've probably already seen, cross promotions keep visitors inside your network, so a visitor to one site is as good as a visitor to another.
You do need quality content if you want any traffic. You also need to serve the customers for each site, cultivate relationships, and capture leads. This is why it's better to have 6 to 8 focused sites than hundreds of unfocused.
So instead of worrying about l inking schemes, just build the best sites you can that serve a specific audience, and associate with those who also serve the same. It will all workout without gimmicks because that is what search engines what from you.
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Justin Hitt helps clients attract more qualified traffic to their business websites, then capture and convert traffic to new customers. For solutions you can use, visit https://www.jwhco.com/