Minor fixes for upcoming version 13

diff --git a/doc/src/sgml/bgworker.sgml b/doc/src/sgml/bgworker.sgml
index 6e1cf121de0..1876dfbd5a5 100644
--- a/doc/src/sgml/bgworker.sgml
+++ b/doc/src/sgml/bgworker.sgml
@@ -34,11 +34,11 @@
   <productname>PostgreSQL</productname> is started by including the module name in
   <varname>shared_preload_libraries</varname>.  A module wishing to run a background
   worker can register it by calling
-  <function>RegisterBackgroundWorker(<type>BackgroundWorker *worker</type>)</function>
+  <function>RegisterBackgroundWorker(<parameter>BackgroundWorker *worker</parameter>)</function>
   from its <function>_PG_init()</function>.  Background workers can also be started
   after the system is up and running by calling the function
-  <function>RegisterDynamicBackgroundWorker(<type>BackgroundWorker
-  *worker, BackgroundWorkerHandle **handle</type>)</function>.  Unlike
+  <function>RegisterDynamicBackgroundWorker(<parameter>BackgroundWorker *worker</parameter>,
+  <parameter>BackgroundWorkerHandle **handle</parameter>)</function>.  Unlike
   <function>RegisterBackgroundWorker</function>, which can only be called from within
   the postmaster, <function>RegisterDynamicBackgroundWorker</function> must be
   called from a regular backend or another background worker.
diff --git a/doc/src/sgml/btree.sgml b/doc/src/sgml/btree.sgml
index d03ee4d6fa0..4a1ac40297c 100644
--- a/doc/src/sgml/btree.sgml
+++ b/doc/src/sgml/btree.sgml
@@ -263,7 +263,7 @@
    </listitem>
   </varlistentry>
   <varlistentry>
-   <term><function>inrange</function></term>
+   <term><function>in_range</function></term>
    <listitem>
     <indexterm>
      <primary>in_range support functions</primary>
diff --git a/doc/src/sgml/intarray.sgml b/doc/src/sgml/intarray.sgml
index 9d2eb52eeb4..956c01d7493 100644
--- a/doc/src/sgml/intarray.sgml
+++ b/doc/src/sgml/intarray.sgml
@@ -452,7 +452,7 @@
 -- a message can be in one or more <quote>sections</quote>
 CREATE TABLE message (mid INT PRIMARY KEY, sections INT[], ...);
 
--- create specialized index with sigature length of 32 bytes
+-- create specialized index with signature length of 32 bytes
 CREATE INDEX message_rdtree_idx ON message USING GIST (sections gist__int_ops(siglen=32));
 
 -- select messages in section 1 OR 2 - OVERLAP operator
diff --git a/src/backend/replication/backup_manifest.c b/src/backend/replication/backup_manifest.c
index b6260049271..a43c793e289 100644
--- a/src/backend/replication/backup_manifest.c
+++ b/src/backend/replication/backup_manifest.c
@@ -272,7 +272,7 @@ AddWALInfoToBackupManifest(backup_manifest_info *manifest, XLogRecPtr startptr,
 	 */
 	if (!found_start_timeline)
 		ereport(ERROR,
-				errmsg("start timeline %u not found history of timeline %u",
+				errmsg("start timeline %u not found in history of timeline %u",
 					   starttli, endtli));
 
 	/* Terminate the list of WAL ranges. */
diff --git a/src/backend/utils/misc/guc.c b/src/backend/utils/misc/guc.c
index 20d4784b335..44c3e5051df 100644
--- a/src/backend/utils/misc/guc.c
+++ b/src/backend/utils/misc/guc.c
@@ -3133,7 +3133,7 @@ static struct config_int ConfigureNamesInt[] =
 	},
 	{
 		{"autovacuum_vacuum_insert_threshold", PGC_SIGHUP, AUTOVACUUM,
-			gettext_noop("Minimum number of tuple inserts prior to vacuum, or -1 to disable insert vacuums"),
+			gettext_noop("Minimum number of tuple inserts prior to vacuum, or -1 to disable insert vacuums."),
 			NULL
 		},
 		&autovacuum_vac_ins_thresh,