I've recently found, that function buttons is called on every animate event. Thus next and prev events are binded so many times, as many times user clicked at navigation buttons.
I suggest to unbind all handlers of prev/next buttons:
/**
* Sets the states of the prev/next buttons.
*
* @method buttons
* @return undefined
*/
buttons: function(n, p) {
if (n == undefined || n == null) {
var n = !this.locked && this.options.size !== 0 && ((this.options.wrap && this.options.wrap != 'first') || this.options.size == null || this.last < this.options.size);
if (!this.locked && (!this.options.wrap || this.options.wrap == 'first') && this.options.size != null && this.last >= this.options.size)
n = this.tail != null && !this.inTail;
}

        if (p == undefined || p == null) {
            var p = !this.locked && this.options.size !== 0 && ((this.options.wrap && this.options.wrap != 'last') || this.first > 1);
            if (!this.locked && (!this.options.wrap || this.options.wrap == 'last') && this.options.size != null && this.first == 1)
                p = this.tail != null && this.inTail;
        }

        var self = this;

/* Start modification /
this.buttonNext.unbind(this.options.buttonNextEvent + '.jcarousel', this.funcNext);
this.buttonPrev.unbind(this.options.buttonPrevEvent + '.jcarousel', this.funcPrev);
/ End modification */
this.buttonNext[n ? 'bind' : 'unbind'](this.options.buttonNextEvent + '.jcarousel', this.funcNext)n ? 'removeClass' : 'addClass'.attr('disabled', n ? false : true);
this.buttonPrev[p ? 'bind' : 'unbind'](this.options.buttonPrevEvent + '.jcarousel', this.funcPrev)p ? 'removeClass' : 'addClass'.attr('disabled', p ? false : true);
},