If the searches are done, then the solicitors will be checking there are no matters arising from those searches. Often the junior staff do the basic legwork but the solicitor has to sign it off so all of a sudden at the end there may be a flurry of requests for proofs of x,y,z.
If you are selling make sure they have ALL the paperwork they need to do with the house, guarantees, certificates of any works done (electrical, damp proofing etc)
Conservatories can be tricky often need a separate questionnaire for those.
Are there any dodgy covenants on the property or dubious rights of way?
Make sure everyone in your chain knows the date you are heading for, & hassle the solicitors ( In a nice but firm way)to make sure they are on the same page for this. Try and avoid ringing them on a Friday, manic on a Friday tying up completions. Often easier to drop an email enquiring how things are going & if there are any other documents needed? Shows willing & reminds them who you are too.
If you are sorted for removals you an exchange & complete on the same day but some folks like them a week apart so they can confirm a provisional day with the removals firm (mine gave me a tip when I last moved pick any day but Friday or Monday if you can!)