Air carrier Captain reported the Final dangerous goods documents provided to the flight crew contained errors. After collaborating with ground personnel and dispatch the flight crew was able to correct the issues and depart safely.

Narrative

Gate XX received initial dangerous goods (DG) via ACARS after 20 minutes of ACARS issues which other aircraft experienced. At approximately XA:29 received the first FINAL DG" report. Inputted the required dangerous goods acknowledgement code into ACARS; and printed out the msg for proof. At approximately XA:43 received a second "FINAL DG" via ACARS; and the report was incomplete. This DG had 3 dry ice entries in the summary section; but only 2 dry ice entries in the expanded explanation section. Attempted to figure it out with ramp via headset standard blue tooth headset issues ensued. Finally heard from ramp that they had held not boarded a section guessed maybe that was the issue but it still should have come up on the report. Tried Operations not much help; eventually the ramp reopened the weight manifest as the FINAL WEIGHT MANIFEST had come out during all of this buffoonery. Searched through FOM for guidance. Found that an item left off should indicate OFF this was not the case. Noticed that an option for pilot request of final DG notification could be obtained another way. Tried that received a report with 3 items in the header portion and 3 items in the expanded section. Entered FINAL dangerous goods acknowledgement code; received ACARS response and THEN did the before push checklist and departed normally; albeit 9 minutes late. Enroute at cruise we debriefed the departure and question arose as to whether it was the FINAL WEIGHT MANIFEST that drove the issue. Went to ACARS LOAD PLAN menu and selected FINAL WEIGHT MANIFEST. A copy of the final printed out automatically as expected; but we also received a copy of the INCORRECT FINAL DG that was sent at XA:43 along with the FINAL WEIGHT MANIFEST. We loaded the PERF INIT to get rid of the execute light after ERASE. This is the second time in the last month out of ZZZ where this Captain has received a second "FINAL" DG notification AFTER submitted dangerous goods acknowledgement code. It is a set up for getting a Captain violated for improper procedures with reference to DG. This Captain treats DG like the Maintenance Release; and pushes back on the hurry hurry hurry mode that exists at the company as we pass the 5 MIN prior to push time.Not sure how to fix this problem the weight and balance as well as DG loading is extremely opaque and after many years still does not make sense at times."