To be able to select my mouse click and drag, do the following:
Set the css property user-select: none; to the element which holds your selectable items.
 
Add on-track="handleTrack" to the element which holds your selectable items.
 
Put this div somewhere in your element: <div id="selectionBox" style="position:absolute; top:0; left:0; height:0; width:0; border:2px solid #000; background-color:rgba(128, 128, 128, 0.3); z-index:999;"></div>
 
Then, add these functions to your element:
handleTrack: function(e) {
    switch(e.detail.state) {
        case "start":
            this.x1 = e.detail.x;
            this.y1 = e.detail.y;
            this.drawRectangle(this.x1, this.y1, this.x2, this.y2);
            break;
        case "track":
            this.x2 = e.detail.x;
            this.y2 = e.detail.y;
            this.drawRectangle(this.x1, this.y1, this.x2, this.y2);
            break;
        case "end":
            this.x2 = e.detail.x;
            this.y2 = e.detail.y;
            this.drawRectangle(0, 0, 0, 0);
            this.selectRectangle(e);
        break;
    }
},
drawRectangle: function(x1, y1, x2, y2) {
    this.$.selectionBox.style.left = x1 + 'px';
    this.$.selectionBox.style.top = y1 + 'px';
    this.$.selectionBox.style.width = (x2 - x1) + 'px';
    this.$.selectionBox.style.height = (y2 - y1) + 'px';
},
selectRectangle: function(e) {
    var tol = 20;
    var ironSelectors = Polymer.dom(e.currentTarget).querySelectorAll("iron-selector");
    ironSelectors.forEach(function(selector) {
        selector.items.forEach(function(i) {
            var el = i.getBoundingClientRect();
            if ((el.left+tol >= this.x1) && (el.top+tol >= this.y1) && (el.right-tol <= this.x2) && (el.bottom-tol <= this.y2)) {
                selector.select(i.value);
            }
        }.bind(this));
    }.bind(this));
}
This code also works if you have multiple iron-selector.