It doesn't seem to impact anything in my app... yet. I'm using the Android support libraries for the first time (my projects to date have not used support libraries), but this is a new project without much in the way of customization yet. Activities were generated by Android Studio 0.9.2 and implement Navigation Drawer.
Running this on a Verizon Samsung Galaxy SIII running Android 4.4.2. Project is set to minSDK of 15 and targeted SDK of 21.
11-21 10:31:18.204 7095-7095/com.myapp.debug I/dalvikvm﹕ Could not find method android.view.ViewGroup.onNestedScrollAccepted, referenced from method android.support.v7.internal.widget.ActionBarOverlayLayout.onNestedScrollAccepted
11-21 10:31:18.204 7095-7095/com.myapp.debug W/dalvikvm﹕ VFY: unable to resolve virtual method 11400: Landroid/view/ViewGroup;.onNestedScrollAccepted (Landroid/view/View;Landroid/view/View;I)V
11-21 10:31:18.204 7095-7095/com.myapp.debug D/dalvikvm﹕ VFY: replacing opcode 0x6f at 0x0000
11-21 10:31:18.204 7095-7095/com.myapp.debug I/dalvikvm﹕ Could not find method android.view.ViewGroup.onStopNestedScroll, referenced from method android.support.v7.internal.widget.ActionBarOverlayLayout.onStopNestedScroll
11-21 10:31:18.204 7095-7095/com.myapp.debug W/dalvikvm﹕ VFY: unable to resolve virtual method 11406: Landroid/view/ViewGroup;.onStopNestedScroll (Landroid/view/View;)V
11-21 10:31:18.204 7095-7095/com.myapp.debug D/dalvikvm﹕ VFY: replacing opcode 0x6f at 0x0000
11-21 10:31:18.204 7095-7095/com.myapp.debug I/dalvikvm﹕ Could not find method android.support.v7.internal.widget.ActionBarOverlayLayout.stopNestedScroll, referenced from method android.support.v7.internal.widget.ActionBarOverlayLayout.setHideOnContentScrollEnabled
11-21 10:31:18.204 7095-7095/com.myapp.debug W/dalvikvm﹕ VFY: unable to resolve virtual method 8977: Landroid/support/v7/internal/widget/ActionBarOverlayLayout;.stopNestedScroll ()V
11-21 10:31:18.204 7095-7095/com.myapp.debug D/dalvikvm﹕ VFY: replacing opcode 0x6e at 0x000e
11-21 10:31:18.234 7095-7095/com.myapp.debug I/dalvikvm﹕ Could not find method android.content.res.TypedArray.getChangingConfigurations, referenced from method android.support.v7.internal.widget.TintTypedArray.getChangingConfigurations
11-21 10:31:18.234 7095-7095/com.myapp.debug W/dalvikvm﹕ VFY: unable to resolve virtual method 368: Landroid/content/res/TypedArray;.getChangingConfigurations ()I
11-21 10:31:18.234 7095-7095/com.myapp.debug D/dalvikvm﹕ VFY: replacing opcode 0x6e at 0x0002
11-21 10:31:18.234 7095-7095/com.myapp.debug I/dalvikvm﹕ Could not find method android.content.res.TypedArray.getType, referenced from method android.support.v7.internal.widget.TintTypedArray.getType
11-21 10:31:18.234 7095-7095/com.myapp.debug W/dalvikvm﹕ VFY: unable to resolve virtual method 390: Landroid/content/res/TypedArray;.getType (I)I
11-21 10:31:18.234 7095-7095/com.myapp.debug D/dalvikvm﹕ VFY: replacing opcode 0x6e at 0x0002
If I'm guessing (and I am), I'm missing a library that android.support.v7 requires. But I have no idea what or where to find it.