As promised, here are the derived characters with which Gauthier (in his 1986 paper) unites Archaeopteryx with modern birds, outside of all other theropods (with Gauthier's original clarifiers in parens) [and with my editorial comments in brackets]:
Premaxillae elongate, narrow, and more pointed anteriorly, with longer nasal processes [similar condition in bullatosaurs, and in the nondinosaurian Megalancosaurus, but unique to Archie and later birds in Maniraptora].
Maxillary process of premaxilla reduced so that maxilla participates broadly in external naris (also in troodontids).
Enlarged brain/basicranium (temporal musculature fails to extend origin onto frontal bones [to a certain degree in bullatosaurs and therizinosauroids, and perhaps in some of the newer, "brainier" dromaeosaurids].
Double-condyled quadrate displaced from distal position on opisthotic to more anteromedial position in contact with prootic (Currie, pers. comm. and Walker, pers. comm., disagree with Whetstone's interpretation of the quadrate: Currie notes the anterior displacement of the quadrate in troodontids [maybe Nino can comment on the condition in Pelecanimimus], and Walker does not consider the quadrate to be double-condyled in Archaeopteryx).
Maxillary and dentary teeth reduced in size and number (or lost), with unserrated crowns and enlarged roots that completely enclose replacement teeth within them [many of the smallest theropod teeth are unserrated, which may be a developmental constraint. The pinched roots of bird teeth are similar to those of troodontids, basal ornithomimosaurs, and (in at least a couple of cases) dromaeosaurids].
Robust furcula for hypertrophied flight musculature [true to a certain extent, although oviraptorids and (perhaps) some dromaeosaurids have substantial furculae as well, and even the new Morrison ?allosaurid seems to have a primitive furcula!].
Scapula with more or less prominent acromion process for ligamentous connection to clavicle.
Lenght/bredth ratio of scapula at midlength exceeds nine (not in penguins) and scapula tapers distally.
Acrocoracoid tuberosity larger than in other coelurosaurs.
Coracoid enlaged and inflected posteromedially more so than in other coelurosaurs.
Very long forelimb and hands (e.g., in Archaeopteryx forelimb is 120-140% of hindlimb length, and more than twice as long as distance between glenoid and acetabulum), with forearm more than 87% of humerus length and mcII approaching or exceeding one-half of humerus length.
Ischium compressed and dorsoventrally deep.
Compared to other theropods, tibia, fibula, and metatarsals relatively more elongate with respect to femur, regardless of body size (mts short in penguins and some other birds) [Actually, as S. Gatsey and I have shown elsewhere, what actually is happening is a difference in the allometry of bird vs nonavian theropod hindlimbs. In nonavian theropods, the tibia/fibula and the metatarsus become relatively smaller as body size (and femur size) increases; in birds, the tibia/fibula and the metarsus become relatively longer as body size (and femur size) increases. Unfortunately, Archaeopteryx lies very close to the points at which the "bird" and "nonbird" allometric lines cross, so it is not possible to say at present to which of these curves the Urvogel belongs].
Fibula attenuate distally, and may not extend to end of tibia.
Proximal tarsals fused to tibia/fibula and to one another in adults [also in some ceratosaurs].
Distal tarsals and metatarsals fused at least distally in fully adult individuals (convergent in some ceratosaurs, elmisaurids, and Hulsanpes) [future work may show why this is no surprise for Hulsanpes...; also found in Avimimus].
First pedal digit elongate and reversed (may be reversed in some extant birds) [the first "reversed" he uses is "reverted"; the second is "reversed" in the evolutinary sense].
Metatarsal I attached on the distal quarter of metatarsal II.
Tail reduced to no more than 23 free caudal vertebrae.
Feathers cover limbs and tail, feathers on lateral margin of tail and posterior margin of arms enlarged, curved, and asymmetrically vaned, indicating aerodynamic function [While it is true these features are currently only known in Archaeopteryx and later birds, there is only negative evidence with regards to this character in other theropods, as discussed in the paragraph immediately following his character list].
Thus, there are derived features linking Archaeopteryx to modern birds. In order to falsify this hypothesis, additional analyses must be conducted which: a) add new characters, or demonstrate that the above are not coded properly; and b) add new taxa, or demonstrate that the taxa previously used were not coded properly. Abundant new discoveries of Mesozoic birds and new bird-like theropods will help on both these counts. With several teams working on just this problem (thankfully not me: nonavian theropods are a problem enough!), we should get some interesting results.