This script looks much more intimidating than the results it produces, so I recommend running it before reading through it.  I’ll run this when I first get on a unfamiliar server as a basic assessment of what’s there and find some hard to find issues with no effort.

The issues you’ll find include:

DECLARE @cutoffdate datetime
DECLARE @use_cutoffdate bit
SET @cutoffdate = DateAdd(Month, -3, GetDate())
SET @use_cutoffdate = 0

IF Object_ID('TempDB..#FileGroupSize') IS NOT NULL BEGIN
	DROP TABLE #FileGroupSize
END

IF Object_ID('TempDB..#DBCC_Temp') IS NOT NULL BEGIN
	DROP TABLE #DBCC_Temp
END

IF Object_ID('TempDB..#DBCC') IS NOT NULL BEGIN
	DROP TABLE #DBCC
END

CREATE TABLE #FileGroupSize
(	  DB VarChar(128)
	, FileGroup VarChar(128)
	, Used_MB Int
	, Free_MB Int
	, Size_MB Int
)

CREATE TABLE #DBCC_Temp 
(
	ParentObject VARCHAR(255),
	[Object] VARCHAR(255),
	Field VARCHAR(255),
	[Value] VARCHAR(255)
)

CREATE TABLE #DBCC
(
	DBName SysName 
	, DBCC_LastGood SmallDateTime
)

exec sp_MSforeachdb N'use [?]; 
INSERT INTO #FileGroupSize
SELECT DB = db_name()
	, FileGroup = ISNULL(g.name, f.Type_Desc) 
	, Used_MB = SUM(FileProperty(f.name, ''SpaceUsed'')) / 128
	, Free_MB = SUM(f.size - FileProperty(f.name, ''SpaceUsed'')) / 128
	, Size_MB = SUM(f.size) / 128 
FROM sys.database_files f
	LEFT JOIN sys.filegroups g on f.data_space_id = g.data_space_id
--WHERE f.Type_Desc = ''LOG''
GROUP BY f.Type_Desc, g.name

TRUNCATE TABLE #DBCC_Temp

INSERT INTO #DBCC_Temp
EXECUTE(''DBCC PAGE ([?], 1, 9, 3)WITH TABLERESULTS'')

INSERT INTO #DBCC
SELECT ''?'', NULLIF([Value],''1900-01-01 00:00:00.000'')
FROM #DBCC_Temp
WHERE Field = ''dbi_dbccLastKnownGood''
'

SELECT database_name = d.name 
	, d.create_date
	, d.compatibility_level
	, #DBCC.DBCC_LastGood
	, LastFullBU = BUFull.last_backup  
	, LastDiffBU = BUDiff.last_backup  
	, LastLogBU = BULog.last_backup  
	, Recovery_Model = d.recovery_model_desc
	, Log_Size_MB = LogSize.Size_MB
	, Log_Pct_Used = Cast(100 * LogSize.Used_MB / (Cast(LogSize.Size_MB as Dec(20,2)) + .01) as Dec(20,2))
	, Data_Size_MB = DataSize.Size_MB
	, Data_Used_MB = DataSize.Used_MB
	, d.collation_name
	, LastFullLoc = BUFullLoc.physical_device_name
	, LastFullSize_MB = Cast(BUFullLoc.backup_size / 1024 / 1024 as bigint)
	--, LastDiffLoc = BUDiffLoc.physical_device_name
	--, LastDiffSize_MB = Cast(BUDiffLog.backup_size / 1024 / 1024 as bigint)
	, LastLogLoc = BULogLoc.physical_device_name
	, LastLogSize_MB = Cast(BULogLoc.backup_size / 1024 / 1024 as bigint)
	, d.is_auto_close_on
FROM master.sys.databases d with (nolock)
	LEFT JOIN (SELECT b.database_name, max(b.backup_finish_date) last_backup
		FROM msdb..backupset b with (nolock)
		WHERE b.type = 'D' 
			AND (b.backup_finish_date > @cutoffdate or @use_cutoffdate = 0)
		GROUP BY b.database_name
		) BUFull ON d.name = BUFull.database_name 
	LEFT JOIN (SELECT b.database_name, max(b.backup_finish_date) last_backup
		FROM msdb..backupset b with (nolock) 
		WHERE b.type = 'I' 
			AND (b.backup_finish_date > @cutoffdate or @use_cutoffdate = 0)
		GROUP BY b.database_name
		) BUDiff ON d.name = BUDiff.database_name 
	LEFT JOIN (SELECT b.database_name, max(b.backup_finish_date) last_backup
		FROM msdb..backupset b with (nolock) 
		WHERE b.type = 'L' 
			AND (b.backup_finish_date > @cutoffdate or @use_cutoffdate = 0)
		GROUP BY b.database_name
		) BULog ON d.name = BULog.database_name 
	LEFT JOIN (SELECT f.physical_device_name, b.database_name, b.backup_finish_date, b.backup_size
		FROM msdb..backupset b with (nolock)
			INNER JOIN msdb..backupmediafamily f ON b.media_set_id = f.media_set_id
		WHERE b.type = 'D') BUFullLoc ON BUFull.database_name = BUFullLoc.database_name AND BUFull.last_backup = BUFullLoc.backup_finish_date
	/*LEFT JOIN (SELECT f.physical_device_name, b.database_name, b.backup_finish_date, b.backup_size
		FROM msdb..backupset b with (nolock)
			INNER JOIN msdb..backupmediafamily f ON b.media_set_id = f.media_set_id
		WHERE b.type = 'I') BUDiffLoc ON BUDiff.database_name = BUDiffLoc.database_name AND BUDiff.last_backup = BUDiffLoc.backup_finish_date
	*/
	LEFT JOIN (SELECT f.physical_device_name, b.database_name, b.backup_finish_date, b.backup_size
		FROM msdb..backupset b with (nolock)
			INNER JOIN msdb..backupmediafamily f ON b.media_set_id = f.media_set_id 
		WHERE b.type = 'L') BULogLoc ON BULog.database_name = BULogLoc.database_name AND BULog.last_backup = BULogLoc.backup_finish_date
	LEFT JOIN (SELECT Size_MB, Used_MB, DB 
				FROM #FileGroupSize 
				WHERE FileGroup = 'Log') LogSize ON d.name = LogSize.DB
	LEFT JOIN (SELECT Size_MB = SUM(Size_MB)
					, Used_MB = SUM(Used_MB)
					, DB 
				FROM #FileGroupSize 
				WHERE FileGroup <> 'Log' 
				GROUP BY DB) DataSize ON d.name = DataSize.DB
	LEFT JOIN #DBCC ON d.name = #DBCC.DBName 
WHERE d.name <> 'tempdb'
	AND d.state = 0 --Online

DROP TABLE #FileGroupSize
DROP TABLE #DBCC_Temp
DROP TABLE #DBCC