According to the script and novelization, Spencer has formed a telepathic link with the twins his wife is carrying. The fetal twins emitted supersonic pulses which tuned with their father's senses. This explains why the alien always managed to track down Jillian whenever she went.
When Spencer and Jillian are at the cocktail reception in New York, Jillian is speaking with the rude woman who criticizes her clothes. As they are walking, they walk past a woman with a large pearl necklace who then kisses the gentleman she is with. Moments later, Jillian walks past the same woman again.
When Spencer checks Jill's pulse at the party, he does it in the wrong place. Pulse is checked below the thumb, while he checks it under Jill's little finger.
When Jill is being examined, she is told she is nine weeks pregnant. However, the baby shown on the ultrasound scan screen is clearly much more than nine weeks old. Furthermore the movements of the ultrasound probe do not correspond to the movements on the screen. And when the doctor says she will make measurements she never does. Instead she just waits a few seconds before announcing the age of the fetus.
Spencer Armacost: Well I told that bloated fast food eating motherfucker that we'd have never gotten the chance to be heroes if he hadn't forced us to put that peice of shit exploding sateliette up into orbit.