1. The Orthodox Church can't settle any contemporary issues; they can't call an ecumenical council without a leader.
In addition to Trisagion's excellent point, not every contemporary issue requires and ecumenical council to address it in the first place. Local/regional councils can deal with problems, too. It is a particularly Roman Catholic conceit to think that some final earthly authority need to be aroused in order for anyone to get anything done, but that has never been the case.
2. The Orthodox Church can't call themselves "Orthodox" because they lack true union with Rome.
We can call ourselves Orthodox because we practice the correct/straight worship and believe in the true Christian doctrine as given to us by our fathers the Apostles and their disciples. We live it every day. That is what makes us Orthodox, not corporeal unity with any one particular church.
3. The Orthodox Church is resisting union with Rome because of ethnic pride.
Thanks to the existence of the Maronites, Italo-Albanians, and the various Rome-affiliated churches that came from subsections of the Nestorian church, there are actually more ethnically/culturally-aligned churches in the Roman communion than there are in either the EO or OO communions. Generally people who make this claim against the Orthodox have not examined their own communion closely enough to see if they might in fact be throwing stones in the proverbial glass house (which they certainly are, if they argue in this manner).
4. The pre-schism Eastern churches would always go to Rome to settle issues.
Nope. Nobody waited around for Rome to pronounce final judgment upon the canons of Constantinople to accept all of them, even as Rome continued to dissent from them. Neither could Rome be counted upon to codify Byzantine canon law at Trullo. Rome was likewise not appealed to in the fight against monothelitism, as it had been accepted by their own Pope, the disgraced Honorius who was anathematized by name in a Chalcedonian ecumenical council quite some time before the Great Schism.
5. Christ established a man, Peter, to be the Rock, and we must be loyal to his successors.
We are, whether that means being loyal to Patriarch John X (Yazigi) or HH Mor Ignatius Zakka I Iwas. Mirroring the above situation regarding "ethnic pride", the Roman Catholics have three Patriarchs connected to this See (one for the Melkites, another for the Maronites, and still another for the Syriac Catholics), so perhaps they should look into their own situation before condemn us.
6. The Orthodox Church has been infiltrated with anti-Roman Protestant converts; many of these converts would have joined us if they could get over their biases. As it is, the Orthodox Church is a safe haven for insincere dissenters.
No doubt this might be true in some cases, but it strikes me as disingenuous, as though those converts by rights should be the "property" of Rome by virtue of the fact that they are Westerners and Rome is the Western apostolic see. If Rome put 1/10th of the energy it puts into bad apologetics like this into restoring the reverence that was once present in its liturgies, conforming itself to true apostolic doctrine and not endless "development of doctrine", etc., this particular objection would vanish entirely (much to the delight of both Catholics and Orthodox, I'm sure), and then nobody would have to pretend to be able to read converts minds. (Incidentally, this kind of thinking also leaves out the many converts from RC-ism to Orthodoxy, such as myself...we are certainly not anti-Roman Protestants, no matter how much some RCs like to comfort themselves by painting us as such!)
7. Doctrines such as papal infallibility and the Immaculate conception were always with the Church in "seed" form; only later did they develop into formal doctrines (see Cardinal Newman).
Lots of things that came to be rejected by the Church can be traced back to ancient times. That doesn't make them right. The development of these rejected doctrines betrays their novelty, even if looking only at them with regard to the Western tradition itself (in other words, you don't even need to bring the Orthodox into it). No less formidable Roman Catholic saints than Bonaventure and Bernard of Clairvaux rejected the doctrine of the Immaculate Conception, for instance, and it is likewise not a secret that catechisms which were published prior to Vatican I, which bore imprimaturs, openly denied Papal Infalliblity (see for instance, Keenan's catechism published in the 1850s, which calls the idea that the Roman Pope is infallible a "Protestant invention").
8. The Orthodox Church has given into ecumenical pressures and allowed divorce and contraception. Only the Catholic Church stands firm on these important moral issues.
They have both by other names (annulments, NFP). Whatever happened to "Let your yes be yes, and your no be no"?
9. The Orthodox are rude to Catholics; they disparage us while we hold our arms open, in hope of their reunion.
Orthodox and Catholics just have very different ideas of what union must consist of. No doubt some could be nicer individuals on both sides, but we are separated for solid doctrinal reasons (i.e., we cannot accept your doctrines for the sake of union with Rome anymore than you can disclaim them for the sake of union with the Orthodox Church), not because of personal vendettas or whatever.
10. Open up a phone book and look at all the Orthodox churches! Russian, Greek, Ukranian. Where's the unity?
This is just point 3 in snarkier language, isn't it? We could say the same: "Look at the Maronite, Ruthenian, Melkite, Syro-Malabar, etc. Catholic churches! Where's the unity?" Ho hum.
11. The Orthodox are inconsistent in their teachings. Some baptize non-Orthodox converts, others don't. Some use an Old Calendar, some use a New Calendar.
Economia and sticking to the guidelines given by their respective synods on how to receive converts is not inconsistency. The Church has always taken a differing approach depending on a person's background, in recognition of the fact that a "one-size-fits-all" rule does not work.
I guess these are not such succinct answers (sorry; as an ex-RC I've dealt with this sort of thing often), but they're what I would say (and have said), or at least keep in mind when evaluating RC apologetics.