Enroute Controller described an Operational Deviation involving a late hand off listing a hurried relief briefing as contributing to the event.

Narrative

I walked up to the sector to relieve a Controller. There were three planes on the Eastern edge of the sector with /3 data blocks and the center aircraft with a 'J-ball'. As these aircraft needed to be at least 5 miles and all at the same altitude they had speeds and turns working. There was a late hand off to ZZZ Sector 10. There may have been more deviations on my part. I am unaware of exactly what occurred. I was handing aircraft off; watching them flash; only to scan back to those aircraft to find them not flashing and it being almost too late. Recommendation; here is the important part. There is supposed to be a shift towards taking responsibility for your work and having pride. The two controllers who set this up; promptly took breaks because they wanted to be on break together. There were many nuances to this situation to include reasons for spacing and coordination's for descending aircraft which were lost in translation. Having said this; it is 100% my responsibility to make sure the sector I take isn't messed up. So; I put all of the blame on my shoulders. In the future; I will be less apt to take a sector this quickly. I have to stop rushing through the briefing; that would help.