Because the Istana is only opened to the public for a few specific days during the year, it is unavoidable that there will be huge crowds going there. One way to beat the crowd is to go early and the weather is also not so hot in the morning. The main problem with the crowd is the queuing up for the security check as well as entering the main hall of the Istana to look at all the impressive exhibits. As for the Istana outdoor compound, there is no problem because it is very spacious and open.
When you are at the front gate of the Istana, you have to queue up for a security check to ensure that you do not bring any dangerous objects into the Istana. Do take note of this as Singapore is very strict against offenders.