That's a very black and white question. Procopius' work in general was a huge game changer when it comes to perception of Justinian's reign, as he is the only major dissident of the regime whose works remained to this day. You must take into account that Procopius was a part of senatorial oligarchy and was opposed to men of low standing like Justin and Justinian, on top of genuine disagreements about policy, such as border defense, loss of autonomy in cities, higher taxes in them (and less money for local projects), treatment of heretics, various "innovations", supposed instability and so on. Some aspects of his criticism, such as the massacre of Nika rioters and the suppression of dissidents, are well attested in other sources, and Procopius is not only well-educated but, as a legal advisor of Belisarius during his campaigns, often well-informed about intricacies of the system and an eyewitness of many major events (like Justinian's plague in Constantinople, where he brings us a first hand account (although his tendency to blame Justinian for it is very questionable)). But when it comes to more personal matters, a large chunk of Procopius' Secret History does follow rhetorical conventions for slander (or invective), and as such the work as a whole has to be taken with a massive grain of salt. It's also important to note that Procopius' other major work, History of the Wars, is likewise full of hidden criticism, which is expressed in typical classical fashion: through omissions and analogies with the classical past. The differences in attitude between Wars, SH and panegyrical Buildings used to leave historians perplexed, but more recent analysis of his works shows surprising degree of consistency for works that were written under vastly different circumstances (Procopius wrote about an emperor who was still alive, and thus had to veil his critique in Wars).

When it comes to personal matters, the situation is fairly complicated. If you're familiar with various invective texts from the classical period, you will run into a fair share of recurring tropes, clichés and so on that appear in Procopius' work as well. An obvious example -- there's one very cursed part about Theodora using all of her holes (to emphasize her promiscuity and thus emasculate her husband, common invective) and cursing god for not giving her a few more -- what's interesting about this is that there are multiple iterations of this exact invective. One is from "On Types of Style" by Hermogenes, which reports a version of the Demosthenic speech "Against Neaera" by Apollodoros of Acharnae where it is said that she "plied her trade through three orifices". But according to Tzetzes, this is an amplification of accusations made by Lysias against Antiope, which was later amplified even further by Procopius. The history of this obvious invective shows that there's little to no truth to it, it's a rhetorical device made to humiliate Theodora, and by extension Justinian. There's also a fair share of references and allusions to earlier sexually themed slander (like Juvenal) as well as some literary tropes from the likes of Aristophanes. Another obvious example would be the narrative about Belisarius. The story goes that Belisarius and Antonina adopted a stepson who essentially cuckolded Belisarius. Belisarius tried to capture and kill him after being in denial for god knows how long despite practically having caught them in the act, but then he was falsely accused of treason and his wife and Theodora plotted and convinced him that Antonina is the reason why he didn't get a death sentence. The chapter itself is called Gynocracy and goes to show Belisarius as an emasculated slave to his wife. This is, by the way, a very common type of slander. Think of Tacitus', Suetonius' and Juvenal's description of Claudius and Messalina. It left such a mark that Messalina became synonymous with an insatiable nympho. For example, slanderers of Catherine the Great called her Messalina of the Neva. Supposed promiscuity of the wife immediately renders the husband weak and incompetent. These slanderous pieces are often inserted to amplify the effect of verifiable, actual policies of Justinian. For example, the BDSM-ish part about Belisarius licking Antonina's feet (also a common element, from Suetonius off the top of my head) is very cleverly placed, as immediately afterwards Procopius goes on with how Justinian introduced proskynesis, something generally associated with Eastern despots (thus, negative connotations in a Roman society). He also makes comparisons and analogies with classical historians writing about, let's say, Cambyses II, as well as comparisons with Khosrow with whom they were warring at the time, and other Easterners. Also comparisons with Domitian, one of the least favorite (if not THE least favorite) Roman Emperors. It was in general pretty common for Roman historians to use past rulers as surrogates for criticism of current ones (Tacitus using Tiberius to criticize Hadrian, Ammianus using Julian for Theodosius I and so on). In his History of the Wars, his criticisms of the ruthless crushing of the Nika riot are expressed merely through parallels with Diodorus Siculus and tyrants of Syracuse.

But in defense of Procopius, it's a historically attested fact that Theodora was an actress, and back then actresses were a profession strongly associated with prostitution, often for a good reason. Most surviving sources ascribe this background to her. Even among monophysite sources, which are favorable of the empress, some like John of Ephesus bring up her problematic past. Whether she actually engaged in prostitution or not is an open question, but it is very likely that she did, and even if she didn't, as a former actress, her social standing before she rose to power was only a notch above prostitutes anyway. Additionally, performing indecent acts on stage, like the ones described by Procopius, would be by no means unusual. Another interesting addition to these claims is that right before he got married to Theodora, Justinian made it legal for the senatorial class to marry prostitutes.

To sum it up, Procopius' Secret History *is* a biased account. It does go out of its way to present Justinian, Theodora, Belisarius and Antonina in the worst light imaginable, with a hefty use of slander, invective and rumors in general, often going as far as calling Justinian and Theodora outright demonic. Nonetheless, it certainly also contains a nucleus of truth, but it's very far from something that can be taken for granted.