function processTag(total, tag, associatedTicker) {
    TagFactory.retrieveTickerTags('onlyTags').then(function(data) {
        console.log('onlyTags data',data);

        // Are there selected Tags:
        // Search for tag in tagFactory
        var oldTag=data[tag.term_id];

        // If found, remove tag:
        if (oldTag) {
            removeTag(tag, associatedTicker);
        }
        else {
            // Save the tag if not found or there are not selected tags:
            if (data.length==0 || total < 3) {
                saveTag(tag, associatedTicker);
            }
            // 3 are already selected, display alert:
            else {
                displayAlert('failure', 'Only 3 tags can be monitored at a time.');
            }
        }
    });
}

function processTag(total, tag, associatedTicker) {
    TagFactory.retrieveTickerTags('onlyTags').then(function(data) {
        console.log('onlyTags data',data);

        // Are there selected Tags:
        // Search for tag in tagFactory
        var oldTag=data[tag.term_id];

        // If found, remove tag:
        if (oldTag) {
            removeTag(tag, associatedTicker);
        }
        else {
            // Save the tag if not found or there are not selected tags:
            if (isEmpty(data) || total < 3) {
                saveTag(tag, associatedTicker);
            }
            // 3 are already selected, display alert:
            else {
                displayAlert('failure', 'Only 3 tags can be monitored at a time.');
            }
        }
    });
}

function isEmpty(data)
{
    for (field in data)
    {
        return false;
    }
    return true;
}

Now it's a pitty you cannot receive a hashmap instead of an array, just to save yourself the task of iterate the elements one by one searching for one.

Well, I think of two techniques for optimizing:

function processTag(total, tag, associatedTicker) {
    var foundFlag = false;

    TagFactory.retrieveTickerTags('onlyTags').then(function(data) {
    console.log('onlyTags data',data);

        // Are there are selected Tags:
        // Search for tag in tagFactory
        var tagIndex=searchTagInArray(data, tag);

        // If found, remove tag:
        if (tagIndex>=0) {
            removeTag(tag, associatedTicker, tagIndex);
        }
        else {
            // Save the tag if not found or there are not selected tags:
            if (data.length==0 || total < 3) {
                saveTag(tag, associatedTicker);
            }
            // 3 are already selected, display alert:
            else {
                displayAlert('failure', 'Only 3 tags can be monitored at a time.');
            }
        }
    });
}

function searchTagInArray(data, tag){
    var foundIndex=-1;
    for (var i=0; foundIndex<0 && i<data.length; i++) {
        if (data[i].term_id === tag.term_id) {
            foundIndex = true;
        }
    }
    return foundIndex;
}

Well, I think of two techniques for optimizing:

    function processTag(total, tag, associatedTicker) {
    var foundFlag = false;

    TagFactory.retrieveTickerTags('onlyTags').then(function(data) {
    console.log('onlyTags data',data);

        // Are there are selected Tags:
        // Search for tag in tagFactory
        var tagIndex=searchTagInArray(data, tag);

        // If found, remove tag:
        if (tagIndex>=0) {
            removeTag(tag, associatedTicker, tagIndex);
        }
        else {
            // Save the tag if not found or there are not selected tags:
            if (data.length==0 || total < 3) {
                saveTag(tag, associatedTicker);
            }
            // 3 are already selected, display alert:
            else {
                displayAlert('failure', 'Only 3 tags can be monitored at a time.');
            }
        }
    });
}

function searchTagInArray(data, tag){
    var foundIndex=-1;
    for (var i=0; foundIndex<0 && i<data.length; i++) {
        if (data[i].term_id === tag.term_id) {
            foundIndex = true;
        }
    }
    return foundIndex;
}

And if you can replace the array for a HashMap, you can save the whole searchTagInArray method:

(Assuming retrieveTickerTags returns data as a HashMap of tags indexed by term_id: data={term0: tag0, term1: tag1, term2: tag2...})

function processTag(total, tag, associatedTicker) {
    TagFactory.retrieveTickerTags('onlyTags').then(function(data) {
        console.log('onlyTags data',data);

        // Are there selected Tags:
        // Search for tag in tagFactory
        var oldTag=data[tag.term_id];

        // If found, remove tag:
        if (oldTag) {
            removeTag(tag, associatedTicker);
        }
        else {
            // Save the tag if not found or there are not selected tags:
            if (data.length==0 || total < 3) {
                saveTag(tag, associatedTicker);
            }
            // 3 are already selected, display alert:
            else {
                displayAlert('failure', 'Only 3 tags can be monitored at a time.');
            }
        }
    });
}