Index: src/js/media/views/settings/attachment-display.js
===================================================================
--- src/js/media/views/settings/attachment-display.js	(revision 47239)
+++ src/js/media/views/settings/attachment-display.js	(working copy)
@@ -83,6 +83,9 @@
 		}
 
 		$input.closest( '.setting' ).removeClass( 'hidden' );
+		if ( $input.length ) {
+			$input[0].scrollIntoView();
+		}
 	}
 });
 
Index: src/wp-includes/css/media-views.css
===================================================================
--- src/wp-includes/css/media-views.css	(revision 47239)
+++ src/wp-includes/css/media-views.css	(working copy)
@@ -346,7 +346,7 @@
 	right: 0;
 	bottom: 0;
 	width: 267px;
-	padding: 0 16px 24px;
+	padding: 0 16px;
 	z-index: 75;
 	background: #f3f3f3;
 	border-left: 1px solid #ddd;
@@ -354,6 +354,17 @@
 	-webkit-overflow-scrolling: touch;
 }
 
+/*
+ * Implementation of bottom padding in overflow content differs across browsers,
+ * we need a different method. See https://github.com/w3c/csswg-drafts/issues/129
+ */
+.media-sidebar::after {
+	content: "";
+	display: flex;
+	clear: both;
+	height: 24px;
+}
+
 .hide-toolbar .media-sidebar {
 	bottom: 0;
 }
@@ -1862,7 +1873,7 @@
 .media-modal .imgedit-wrap .imgedit-settings {
 	background: #f3f3f3;
 	border-left: 1px solid #ddd;
-	padding: 20px 16px 16px;
+	padding: 20px 16px 0;
 	position: absolute;
 	top: 0;
 	right: 0;
@@ -1871,6 +1882,17 @@
 	overflow: auto;
 }
 
+/*
+ * Implementation of bottom padding in overflow content differs across browsers,
+ * we need a different method. See https://github.com/w3c/csswg-drafts/issues/129
+ */
+.media-modal .imgedit-wrap .imgedit-settings::after {
+	content: "";
+	display: flex;
+	clear: both;
+	height: 16px;
+}
+
 .media-modal .imgedit-group {
 	background: none;
 	border: none;
@@ -2001,10 +2023,22 @@
 	left: 0;
 	right: 0;
 	bottom: 0;
-	padding: 0 16px 32px;
+	padding: 0 16px;
 	overflow: auto;
 }
 
+/*
+ * Implementation of bottom padding in overflow content differs across browsers,
+ * we need a different method. See https://github.com/w3c/csswg-drafts/issues/129
+ */
+.embed-link-settings::after,
+.embed-media-settings::after {
+	content: "";
+	display: flex;
+	clear: both;
+	height: 24px;
+}
+
 .media-embed .embed-link-settings {
 	/* avoid Firefox to give focus to the embed preview container parent */
 	overflow: visible;
@@ -2049,6 +2083,10 @@
 	padding: 0;
 }
 
+.image-details .embed-media-settings::after {
+	content: none;
+}
+
 .image-details .embed-media-settings,
 .image-details .embed-media-settings div {
 	box-sizing: border-box;