A friend of mine had the same issue and contacted Ilford customer support. The relevant parts from the reply he got are:
“I'm sorry you've been alarmed by some abnormal looking dark and lights spots on your processed MGFB paper. From your helpful description - I can put your mind at rest, as I am recognising the exact issue you describe.
The issue only affects FB (never RC) and only ever shows when FB paper is wet. It can arise on all FB products, and on all/random batches. Exact as you report - it can show as dark spots seen on the base side when wet only. But also as light spots - on the emulsion side, again only when wet. The spots often show worse if you hold a wet print up to lights/a window - or over a lightbox.
The issue is linked to an enforced base change approx 4 years ago (This is why they weren't present on the prior product version - MGFB IV). The newer base has a slightly different paper structure/fibre weave, and this means some of the paper pulp can show more openly - and with more structure when wet. Prior to the base change, these sorts of spots were rarely ever seen. The issue if it shows, really is very random though.
Following all investigations and from the feedback of customers - our findings are that these spots really do only show when wet, and they have no adverse effects in dried prints. Nor do they alter archival stability of prints. So any prints you're seeing these spots on when wet, will be as archivally stable as prints pre the base change, and the spots ought not ever show. You won't need to alter anything either - re how you process your prints.
Just in case it further helps, the issue can tend to show more when prints are washed longer than we guide, but even then - they are never showing when try, and still don't affect archival stability.”