How do I find which objects that were analyzed during an autostats job?

Step 1

Find the start and stop times of the maintenance window:

select window_name, cast(last_start_date as date) "Start Time", DURATION, cast(last_start_date+duration as date) "End Time"
FROM DBA_SCHEDULER_WINDOWS
WHERE ENABLED='TRUE'
AND WINDOW_NAME LIKE UPPER('%&&day%');

Which results in:

WINDOW_NAME	Start Time	DURATION	End Time
WEDNESDAY_WINDOW	18.04.2018 23:59:00	+00 04:00:00.000000	19.04.2018 03:59:00

So my Wednesday window starts at 23:59 and ends 4 hours later, at 03:59.

Step 2
Add the query above as a subquery in a query against DBA_OPTSTAT_OPERATIONS, to get all the IDs for the sub-steps that was executed during this window:

select ID
from DBA_OPTSTAT_OPERATIONS 
where operation='gather_database_stats (auto)' 
and CAST(start_time AS DATE) BETWEEN 
                                ( SELECT CAST (LAST_START_DATE AS DATE)
                                  FROM  DBA_SCHEDULER_WINDOWS
                                  WHERE ENABLED='TRUE'
                                  AND   WINDOW_NAME LIKE UPPER('%&&day%')
                                 )
                              AND 
                                 (
                                  SELECT CAST (LAST_START_DATE+DURATION AS DATE)
                                  FROM  DBA_SCHEDULER_WINDOWS
                                  WHERE ENABLED='TRUE'
                                  AND   WINDOW_NAME LIKE UPPER('%&&day%')
                                 )
;

Step 3
Put everything together by querying DBA_OPTSTAT_OPERATION_TASKS, to see which tasks and which objects that were analyzed during the time window:

-- get the details for every task executed by "gather_database_stats (auto)" 
SELECT opid,
       target,
       target_objn,
       target_type,
       target_size,
       cast(start_time as date) "Start Time",
       cast(end_time as date) "End Time", 
       status
FROM DBA_OPTSTAT_OPERATION_TASKS 
WHERE OPID IN ( -- get the unique ID for the "gather_database_stats (auto)" jobs
                SELECT ID FROM DBA_OPTSTAT_OPERATIONS 
                WHERE OPERATION='gather_database_stats (auto)' 
                AND CAST (START_TIME AS DATE) BETWEEN 
                                                -- get the start and stop times for the last window
                                                -- for a particular weekday
                                                (SELECT CAST(LAST_START_DATE AS DATE)
                                                      FROM DBA_SCHEDULER_WINDOWS
                                                      WHERE ENABLED='TRUE'
                                                      AND WINDOW_NAME LIKE UPPER('%&&day%')
                                                     )
                                                AND (
                                                      SELECT CAST(LAST_START_DATE+DURATION AS DATE)
                                                      FROM DBA_SCHEDULER_WINDOWS
                                                      WHERE ENABLED='TRUE'
                                                      AND WINDOW_NAME LIKE UPPER('%&&day%')
                                                     )
)
order by CAST(start_time as DATE) asc;

Sample output (displaying the first and last 5 rows of the record set):

OPID	TARGET	TARGET_OBJN	TARGET_TYPE	TARGET_SIZE	Start Time	End Time	STATUS
48848	SYS.ET$16E30DF80001	6177051	TABLE	0	18.04.2018 23:59:30	18.04.2018 23:59:30	FAILED
48848	SYS.I_SEQ1	79	INDEX	1	18.04.2018 23:59:30	18.04.2018 23:59:31	COMPLETED
48848	SYS.SEQ$	74	TABLE	7	18.04.2018 23:59:30	18.04.2018 23:59:31	COMPLETED
48848	SYS.OPTSTAT_HIST_CONTROL$	506	TABLE	1	18.04.2018 23:59:31	18.04.2018 23:59:31	COMPLETED
48848	SYS.REG$	5775	TABLE	1	18.04.2018 23:59:31	18.04.2018 23:59:31	COMPLETED
...
48885	SYS.WRH$_SERVICE_STAT.WRH$_SERVICE_STAT_2490506650_826	11986128	TABLE PARTITION	5	19.04.2018 02:00:48	19.04.2018 02:00:48	COMPLETED
48885	SYS.WRH$_SEG_STAT_PK.WRH$_SEG_STAT_2490506650_826	11986126	INDEX PARTITION	1	19.04.2018 02:00:48	19.04.2018 02:00:48	COMPLETED
48885	SYS.WRH$_SGASTAT_U.WRH$_SGASTAT_2490506650_826	11986114	INDEX PARTITION	1	19.04.2018 02:00:48	19.04.2018 02:00:48	COMPLETED
48885	SYS.WRH$_SEG_STAT.WRH$_SEG_STAT_2490506650_826	11986124	TABLE PARTITION	5	19.04.2018 02:00:48	19.04.2018 02:00:48	COMPLETED
48885	SYS.WRH$_SEG_STAT.WRH$_SEG_STAT_2490506650_826	11986124	TABLE PARTITION	5	19.04.2018 02:00:48	19.04.2018 02:00:48	COMPLETED

Check the overall status of your run:

SELECT target_type,status,count(*)
FROM DBA_OPTSTAT_OPERATION_TASKS 
WHERE OPID IN ( -- get the unique ID for the "gather_database_stats (auto)" jobs
                SELECT ID FROM DBA_OPTSTAT_OPERATIONS 
                WHERE OPERATION='gather_database_stats (auto)' 
                AND CAST(START_TIME AS DATE) BETWEEN 
                                                -- get the start and stop times for the last window
                                                -- for a particular weekday
                                                (SELECT CAST(LAST_START_DATE AS DATE)
                                                      FROM DBA_SCHEDULER_WINDOWS
                                                      WHERE ENABLED='TRUE'
                                                      AND WINDOW_NAME LIKE UPPER('%&&day%')
                                                     )
                                                AND (
                                                      SELECT CAST(LAST_START_DATE+DURATION AS DATE)
                                                      FROM DBA_SCHEDULER_WINDOWS
                                                      WHERE ENABLED='TRUE'
                                                      AND WINDOW_NAME LIKE UPPER('%&&day%')
                                                     )
)
group by target_type,status
order by status;

Result:

TARGET_TYPE	STATUS	COUNT(*)
INDEX	COMPLETED	501
INDEX PARTITION	COMPLETED	177
TABLE	COMPLETED	394
TABLE PARTITION	COMPLETED	362
TABLE	FAILED	54

To further filter out those objecs that failed, use:

SELECT distinct target,target_objn,target_type
FROM DBA_OPTSTAT_OPERATION_TASKS 
WHERE OPID IN ( -- get the unique ID for the "gather_database_stats (auto)" jobs
                SELECT ID FROM DBA_OPTSTAT_OPERATIONS 
                WHERE OPERATION='gather_database_stats (auto)' 
                AND CAST(START_TIME AS DATE) BETWEEN 
                                                -- get the start and stop times for the last window
                                                -- for a particular weekday
                                                (SELECT CAST(LAST_START_DATE AS DATE)
                                                      FROM DBA_SCHEDULER_WINDOWS
                                                      WHERE ENABLED='TRUE'
                                                      AND WINDOW_NAME LIKE UPPER('%&&day%')
                                                     )
                                                AND (
                                                      SELECT CAST(LAST_START_DATE+DURATION AS DATE)
                                                      FROM DBA_SCHEDULER_WINDOWS
                                                      WHERE ENABLED='TRUE'
                                                      AND WINDOW_NAME LIKE UPPER('%&&day%')
                                                     )
)
AND status = 'FAILED'
order by TARGET;

Which in my case revealed that the following objects need attention:

TARGET	TARGET_OBJN	TARGET_TYPE
SYS.ET$16E30DF80001	6177051	TABLE
SYS.X$LOGMNR_CONTENTS	4294951535	TABLE
SYS.X$LOGMNR_REGION	4294951631	TABLE