Can I select multiple tags using getElementsByTagName?

A year late, but if you intend on using the desired functionality multiple times in your project, and you don't have access to querySelector(), it might be worth extending the Node object with a simple function:

JavaScript

/**
 * @param {Array} tags - The array of tagNames to search for.
 * @return {Array}     - The elements with matching tagNames.
 */
Node.prototype.getElementsByTagNames = function (tags) {
    var elements = [];

    for (var i = 0, n = tags.length; i < n; i++) {
        // Concatenate the array created from a HTMLCollection object
        elements = elements.concat(Array.prototype.slice.call(this.getElementsByTagName(tags[i])));
    }

    return elements;
};

Working demo on JSFiddle.

All it does is iterating over an array of tag names, then getting the corresponding elements using getElementsByTagName() for each iteration.

This can then of course be used on any element the same exact way you use similar functions - for example, getElementById() - on any Node object, you are not limited to document.

No, you can't select multiple tags with a single call to getElementsByTagName. You can either do two queries using getElementsByTagName or use querySelectorAll.

JSFiddle

var elems = document.querySelectorAll('p,li')