The 6th-level cleric spell animate objects [trans] (Player's Handbook 199), in part, says that after it's cast that the "animated object then immediately attacks whomever or whatever you initially designate" and that the caster "can change the designated target or targets as a move action, as if directing an active spell" (ibid.). (Also see Direct or Redirect a Spell (PH 143).)
The 1st-level Sor/Wiz spell summon monster I [conj] (PH 285–6, 287) that says, "If you can communicate with the creature [that you've summoned via the spell], you can direct it not to attack, to attack particular enemies, or to perform other actions" (286). The spell animate objects includes no such language. This should make it impossible to order an object animated by the spell animate objects to do anything but attack the first target or another designated target.
(Rules lawyers—among whom I sometimes count myself—would argue that this makes ordering an object animated by the animate objects spell not to attack is impossible! For example, if the caster just wants the animated object to travel over there, the caster needs to direct the object animated by the animate objects spell to attack a target over there! Also keep in mind that—for reasons that I can't fathom—the animate objects spell isn't dismissible therefore—literally, mind you—objects so animated automatically keep on attacking for the spell's duration until the spell's duration expires or a dispel magic effect is successfully used on them! (Also see this Pathfinder question that's identical in 3.5.) To this DM, player, and general reader, that seems extraordinarily restrictive, especially in light of the spell's spell level.)
However, the spell also says, "The Monster Manual has game statistics for animated objects" (199), and the Monster Manual on Animated Object, in part, says, that they "owe their existence as creatures to spells such as animate objects or similar supernatural abilities" (13) like the supernatural ability animate objects of the ravid (214). Further, Animated Object on Combat says, "Animated objects fight only as directed by the animator. They follow orders without question and to the best of their abilities" (13).
To be clear, the Player's Handbook only directs the reader to the Monster Manual for an animated object's statistics, making it so that bit about the animated objects doing their best to follow orders unquestioningly could be safely ignored… except that actually determining an animated object's statistics requires reading that Combat section, and that section includes the bit about the animated objects doing their best to follow orders unquestioningly!
Thus, unless the DM rules that when the Monster Manual says that animated objects "follow orders without question and to the best of their abilities" that the Monster Manual really means that animated object follow orders about what to attack without question and to the best of their abilities—which is, again, quite a restrictive reading—, there's an impasse.
The Player's Handbook is the primary source for spells like the spell animate objects, and the Monster Manual is the primary source for monsters like the animated object, and the two contradict each other on whether an object animated by the animate objects spell can perform tasks other than attacking. (Also see this question.) This means the DM must adjudicate which takes precedence. If it's the Player's Handbook, then objects animated by the animate objects spell can only attack, but if it's the Monster Manual, then—under a not-so-restrictive reading—objects animated by the animate objects spell follow the caster's orders to the best of their abilities unquestioningly, whatever those orders may be.
A compromise position
In this DM's campaigns, the objects animated by the spell animate objects can only be ordered to attack. (They can also be ordered not to attack because if they can't that's weird, darn it!) On the other hand, when objects animated by the spell animate objects will exist long-term via, for example, the 5th-level Sor/Wiz spell permanency [univ] (PH 259–60), this DM allows the caster of the animate objects spell to, thereafter, issue orders to the objects that they then do their best to follow unquestioningly. This has worked out for this DM fine in play, even at low levels. (A PC in a campaign I ran had levels in a homebrew class that granted the spell animate objects as a 1st-level spell, so this has actually come up in play. Honestly, most clerics that are level 11 or higher just aren't going to bother with the animate objects spell because they have so many better options; this makes assessing the spell in its original context more difficult.)
Note: While differences exist between the 3.5 spell and the 3.5 monster and the pre-revision spell animate objects and the pre-revision monster animated object in, respectively, the Player's Handbook (2000) and Monster Manual (2000), this contradiction also existed even in the game's original state.