It is probably this bug https://code.google.com/p/dart/issues/detail?id=18062 you run into.
Workaround in the meantime is to set via dart:js (using repro from #9):
import 'dart:html';
import 'dart:js';
void main() {
var ta = new TextAreaElement();
ta.wrap = "off";
document.body.children.add(ta);
ta.text = "abcde 01234 (1) abcde 01234 (2) abcde 01234 (3) abcde 01234 (4) "
"abcde 01234 (5) abcde 01234 (6) abcde 01234 (7) abcde 01234 (8) ";
new JsObject.fromBrowserObject(ta)['scrollLeft'] = '200';
}