Theme Issue

It looks like the theme content div has overflow set to hidden. There are a few options:

Modify the theme style.css file (or create a child theme) and remove (or comment-out) the overflow property:

.post-content {
    padding-top: 15px;
    margin-top: 15px;
    padding-bottom: 15px;
    margin-bottom: 15px;
    /* overflow: hidden; */
    clear: both;
}

Or, modify the theme style.css file to modify the NWS Alerts styles:

.nws-alerts {
    float:none;
}
.nws-alerts-heading {
    float:none;
}
.nws-alerts-details {
    position:relative;
    display:block;
    max-height:none;
    height:auto;
    opacity:1;
}
.nws-alerts-entries {
    max-height:none;
    height:auto;
}

Let me know if neither of these will work.

I forgot to include the mouse-over styles, so you’ll want to add this to the bottom of what you’ve already added. This will prevent the height from being restricted on mouse-over, so the glitches will go away.

.nws-alerts:hover {
    z-index:3;
}
.nws-alerts:hover .nws-alerts-entries {
    max-height:none;
}

Depending on your needs you may also want to make the map larger and you can do that by adjusting the height with the below selector:

.nws-alerts-map {
    height: 400px;
}