diff --git a/.errcheck-excludes b/.errcheck-excludes
index 524ce5a3ba..c46637a908 100644
--- a/.errcheck-excludes
+++ b/.errcheck-excludes
@@ -2,3 +2,6 @@
 (github.com/mongodb/mongo-go-driver/core/connection.Connection).Close
 (*github.com/mongodb/mongo-go-driver/core/topology.Subscription).Unsubscribe
 (*github.com/mongodb/mongo-go-driver/core/topology.Server).Close
+(*github.com/mongodb/mongo-go-driver/core/connection.pool).closeConnection
+(net.Conn).Close
+encoding/pem.Encode
diff --git a/Makefile b/Makefile
index 0b91e55f7f..b34d893bf4 100644
--- a/Makefile
+++ b/Makefile
@@ -39,7 +39,7 @@ lint-add-whitelist:
 
 .PHONY: errcheck
 errcheck:
-	errcheck -exclude .errcheck-excludes ./bson/... ./mongo/...
+	errcheck -exclude .errcheck-excludes ./bson/... ./mongo/... ./core/...
 
 .PHONY: test
 test:
diff --git a/core/examples/cluster_monitoring/main.go b/core/examples/cluster_monitoring/main.go
index 2c7df91eaa..35b75d64af 100644
--- a/core/examples/cluster_monitoring/main.go
+++ b/core/examples/cluster_monitoring/main.go
@@ -19,7 +19,10 @@ func main() {
 	if err != nil {
 		log.Fatalf("could not create topology: %v", err)
 	}
-	topo.Connect(context.Background())
+	err = topo.Connect(context.Background())
+	if err != nil {
+		log.Fatalf("could not create topology: %v", err)
+	}
 
 	sub, err := topo.Subscribe()
 	if err != nil {
diff --git a/core/examples/count/main.go b/core/examples/count/main.go
index 4d17c62a19..698e4bbd20 100644
--- a/core/examples/count/main.go
+++ b/core/examples/count/main.go
@@ -42,7 +42,10 @@ func main() {
 	if err != nil {
 		log.Fatal(err)
 	}
-	t.Connect(context.Background())
+	err = t.Connect(context.Background())
+	if err != nil {
+		log.Fatal(err)
+	}
 
 	ctx, cancel := context.WithTimeout(context.Background(), 30*time.Second)
 	defer cancel()
diff --git a/core/topology/initial_dns_seedlist_discovery_test.go b/core/topology/initial_dns_seedlist_discovery_test.go
index 682f242365..07cdac60bb 100644
--- a/core/topology/initial_dns_seedlist_discovery_test.go
+++ b/core/topology/initial_dns_seedlist_discovery_test.go
@@ -92,7 +92,8 @@ func runSeedlistTest(t *testing.T, filename string, test *seedlistTestCase) {
 		// make a topology from the options
 		c, err := New(WithConnString(func(connstring.ConnString) connstring.ConnString { return cs }))
 		require.NoError(t, err)
-		c.Connect(context.Background())
+		err = c.Connect(context.Background())
+		require.NoError(t, err)
 
 		for _, host := range test.Hosts {
 			_, err := getServerByAddress(host, c)
diff --git a/core/topology/topology.go b/core/topology/topology.go
index 871175fb42..d68fd54f2f 100644
--- a/core/topology/topology.go
+++ b/core/topology/topology.go
@@ -367,7 +367,7 @@ func (t *Topology) apply(ctx context.Context, desc description.Server) (descript
 	}
 
 	for _, added := range diff.Added {
-		t.addServer(ctx, added.Addr)
+		_ = t.addServer(ctx, added.Addr)
 	}
 	t.serversLock.Unlock()
 	return current, nil