Obito's left Sharingan is in posession of Hatake Kakashi, so let's compare Obito with Kakashi and the other known Uchihas.
To use Mangekyou Sharingan Kakashi needs to accumulate a lot of chakra before he can use Kamui on Deidara's arm. The size of the object determines the amount of chakra he needs as seen in the case where he tried to blow the neck of Juubi with that jutsu (thus, Sahan De Silva's comment is not very correct). Since he is not an Uchiha, he requires a lot more chakra and puts more burden on him than it should be as he himself mentioned. Kakashi also suffered the side effect of overusing the Mangekyou Sharingan which he mentioned during the fight between him and Sasuke.
Itachi was seen bleeding when using his Mangekyou Sharingan, especially when he use Amaterasu. This is due to the strain the jutsu puts on the eye. Itachi also suffers the other side effects of losing eyesight and is in pain when using it, although since he was dying at the time he was fighting Sasuke, it can also be said that the pain is also from him over-exerting himself.
Sasuke also suffered the same side effect of losing eyesight and bleeding when using Amaterasu, much like Itachi was. Since Sasuke was healthy and not sickly like Itachi, it can be determined that overusing Mangekyou Sharingan puts the user in pain. He later recovered from it by transplanting Itachi's eyes and gained the Eternal Mangekyou Sharingan.
Uchiha Madara also suffered the same side effect and was thus forced to take his brother's eyes. He no longer get the negative side effects after awakening his Eternal Mangekyou Sharingan.
Now, based on this fact, the only difference Obito has compared to the other Mangekyou Sharingan users is that he possessed the Senju DNA. The conclusion is, Obito didn't suffer the negative side effects of the Mangekyou Sharingan due to the Senju DNA he possessed.