I'm going to write this from the perspective of US law, as that's what I know most about. @experiencethis, if you're located outside the US, please let us know so that we can work to find a community member with experience or knowledge in your neck of the woods.
Alright, the usual disclosures: I am not a lawyer, this is not legal advice. This is my personal understanding of Intellectual Properly (IP) fair use law. If you really want to know the answer, consult with an IP lawyer.
The concept of fair use in the United States is paramount in IP. Fair use is defined as "any copying of copyrighted material done for a limited and 'transformative' purpose, such as to comment upon, criticize, or parody a copyrighted work."
Judges usually consider four factors when considering fair use cases:
1. The purpose and character of your use
2. The nature of the copyrighted work
3. The amount and substantiality of the portion taken, and
4. The effect of the use upon the potential market.
Let's take a quick look at each of these individual factors.
The purpose and character of your use
Judges generally look at whether your work is being used to create something new, or simply as a guise to reproduce IP verbatim. Courts look to see if your work transforms the original piece by adding new meaning or value. They also look if you're adding value by changing aesthetics or adding insight or understanding.
In this sense, using IP in your portfolio to critically examine the journey of an app or website would be permissible. You are adding insight and understanding to the IP by critically examining the process that was used to create it.
The nature of the copyrighted work
This doesn't apply as heavily in our use case, as this concept generally deals with whether or not the work was fiction/non-fiction. Judges look more favorably on reproduction of non-fiction work as it is commonly used to disseminate facts to the public. Conversely, fictional work is usually seen as having the sole puprose of entertainment. This provides less social value.
However, also examined here is whether or not a work is published or unpublished. Published, publicly available work has much more leeway with fair use than unpublished work. I'm assuming you'd only be using published sites and materials.
So far, we're 2/2 on our tests.
The amount and substantiality of the portion taken
Simply put, the less you take the more likely you are to avoid issues. In terms of examining a site, this means that you're more likely to have success by examining a particular page, workflow, or section of a site, rather than the site as a whole.
Effect of the use upon the potential market
This aspect looks at whether or not the use of someone else's IP potentially blocks the IP holder from financial gain. In general, this has to do with whether or not the work you produce is related or competitive.
When using IP in context of a site review, it's clear you're not looking to compete with the IP holder. You are not producing competitive work. The only way you might block the IP holder from financial gain is by pointing out issues with the site. Any suit brought against you would revolve around libel law, not IP law.
The rule of thumb with libel law is much simpler than IP law. Your best defense to a libel suit is the truth.
Summing it up
When reviewing IP in your portfolio, follow a few best practices to avoid potential issues:
1. Limit the scope of your review to a specific page or section of a site.
2. Provide an in-depth examination of the IP to ensure you are adding insight and understanding.
3. Use only content from published, publicly-available websites.
4. When in doubt as to the right to use or acknowledge a source, the most prudent course may be to seek the permission of the copyright owner.
Editing for grammar and such.