diff --git a/blocks/library/image/editor.scss b/blocks/library/image/editor.scss
index 1c12f4f85e754a..de39f03861c23a 100644
--- a/blocks/library/image/editor.scss
+++ b/blocks/library/image/editor.scss
@@ -113,3 +113,14 @@
 		}
 	}
 }
+
+.editor-block-list__block[data-type="core/image"] .editor-block-toolbar .blocks-format-toolbar__link-modal {
+	position: absolute;
+	left: 0;
+	right: 0;
+	margin: -1px 0;
+
+	@include break-small() {
+		margin: -1px;
+	}
+}
\ No newline at end of file
diff --git a/blocks/url-input/style.scss b/blocks/url-input/style.scss
index 73f5840b05af48..3c005f6ea11a2d 100644
--- a/blocks/url-input/style.scss
+++ b/blocks/url-input/style.scss
@@ -42,6 +42,15 @@ $input-size: 230px;
 	width: $input-size + $icon-button-size * 2 + 2px; // add borders
 }
 
+// Hide suggestions on mobile until we @todo find a better way to show them
+.blocks-url-input__suggestions,
+.blocks-url-input .spinner {
+	display: none;
+	@include break-small() {
+		display: inherit;
+	}
+}
+
 .blocks-url-input__suggestion {
 	padding: 4px #{ $icon-button-size + $input-padding } 4px $input-padding;
 	color: $dark-gray-300; // lightest we can use for contrast
diff --git a/editor/components/block-list/style.scss b/editor/components/block-list/style.scss
index bda716bfc0a00d..b9027ef3633821 100644
--- a/editor/components/block-list/style.scss
+++ b/editor/components/block-list/style.scss
@@ -670,10 +670,6 @@
 		margin-left: -1px;
 	}
 
-	> .editor-block-switcher:first-child {
-		margin-left: -2px;
-	}
-
 	@include break-small() {
 		width: auto;
 	}
diff --git a/editor/components/block-switcher/style.scss b/editor/components/block-switcher/style.scss
index dc258edb7b29f6..8a0936e267ca1e 100644
--- a/editor/components/block-switcher/style.scss
+++ b/editor/components/block-switcher/style.scss
@@ -1,5 +1,9 @@
 .editor-block-switcher {
 	position: relative;
+
+	.components-toolbar {
+		border-left: none;
+	}
 }
 
 .editor-block-switcher__toggle {
diff --git a/editor/components/block-toolbar/style.scss b/editor/components/block-toolbar/style.scss
index f015989f05fe04..651a4242b066a5 100644
--- a/editor/components/block-toolbar/style.scss
+++ b/editor/components/block-toolbar/style.scss
@@ -1,9 +1,14 @@
 .editor-block-toolbar {
 	display: inline-flex;
-	overflow: auto; // allow horizontal scrolling on mobile
 	flex-grow: 1;
 	width: 100%;
 	background: $white;
+	overflow: auto; // allow horizontal scrolling on mobile
+
+	// allow overflow on desktop
+	@include break-small() {
+		overflow: inherit;
+	}
 
 	.components-toolbar {
 		border: none;
diff --git a/editor/components/observe-typing/index.js b/editor/components/observe-typing/index.js
index 9ba35d7ce7d2ef..1ebe6a22c83bb8 100644
--- a/editor/components/observe-typing/index.js
+++ b/editor/components/observe-typing/index.js
@@ -120,7 +120,8 @@ class ObserveTyping extends Component {
 
 		// Abort early if already typing, or key press is incurred outside a
 		// text field (e.g. arrow-ing through toolbar buttons).
-		if ( isTyping || ! isTextField( target ) ) {
+		// Ignore typing in a block toolbar
+		if ( isTyping || ! isTextField( target ) || target.closest( '.editor-block-toolbar' ) ) {
 			return;
 		}