Google ranks websites (relevancy aside for a moment) by the number and quality of incoming links to a site from other websites (amongst hundreds of other metrics). Generally speaking, a link from a page to another page is viewed in Google “eyes” as a vote for that page the link points to. The more votes a page gets, the more trusted a page can become, and the higher Google will rank it – in theory. Rankings are HUGELY affected by how much Google ultimately trusts the DOMAIN the page is on. BACKLINKS (links from other websites – trump every other signal.)
When would this be useful? If your site has a blog with public commenting turned on, links within those comments could pass your reputation to pages that you may not be comfortable vouching for. Blog comment areas on pages are highly susceptible to comment spam. Nofollowing these user-added links ensures that you're not giving your page's hard-earned reputation to a spammy site.
If a PARTICULAR CANONICAL HEAD KEYWORD is IMPORTANT (even perhaps a SYNONYM or LONG TAIL VARIANT) and I think a particular 301 REDIRECT has some positive impact on how Google judges the quality or relevance the page, I will make sure the CANONICAL HEAD KEYWORD and SYNONYMS are on the FINAL PAGE I redirect Google to (which is the one that will be rated and cached).
An SEO audit should not be rushed. It simply takes time to uncover root causes of the issues affecting your online health. Depending on the size of your site, a proper audit can take anywhere from 2-6 weeks to complete. Due diligence is required when making major changes to any website, and an SEO specialist must conduct a thorough investigation to make accurate, impactful recommendations.