Recently my client has configured HTTPS. I recommended that he implement 301 redirection to 200. His developer could not do that and it is still using 302 redirects.
How bad it can affect a website if it uses 302 redirects?
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Whilst I'd definitely always 301 http to https (as why would it ever be temporary?), Google have said that 301, 302, 30x do not dilute your pagerank in SEO.
The team at MOZ have recently studied this, and IIRC they're not so convinced.
If it was my site, I'd definitely tell/bribe whoever did your 302s, and get them to do 301s.
It is not good to have those redirects as a 302. Google's indexing will keep those old HTTP URLs, as the 302 redirect is a "Temp" redirect. The HTTPS pages will still index, but may compete with the HTTP pages, that or the HTTPS may struggle to index. Would be also concerned if there is a canonical link elements on the pages and if so, what version they point to... ie HTTP or HTTPS.
If the developer can't set the redirects to a 301, then you need a new developer. It should be a simple adjustment.