There is a long story about this topic, going back to its first introduction in the 1950s. It probably doesn't help that you can crank up the power on an ultrasonic device to do things like break up kidney stones; surely, such technology must come with tradeoffs, like X-rays do.
A large, longitudinal study reported in 1993 with 15,151 pregnant mothers as subjects found that:
The mean numbers of sonograms obtained per woman in the ultrasound-screening and control groups were 2.2 and 0.6, respectively. The rate of adverse perinatal outcome was 5.0 percent among the infants of the women in the ultrasound-screening group and 4.9 percent among the infants of the women in the control group (relative risk, 1.0; 95 percent confidence interval, 0.9 to 1.2; P = 0.85). The rates of preterm delivery and the distribution of birth weights were nearly identical in the two groups. The ultrasonographic detection of congenital anomalies had no effect on perinatal outcome. There were no significant differences between the groups in perinatal outcome in the subgroups of women with post-date pregnancies, multiple-gestation pregnancies, or infants who were small for gestational age.
They did define 'adverse perinatal outcome' as:
Adverse perinatal outcome was defined as fetal death, neonatal death, or neonatal morbidity such as intraventricular hemorrhage.
Which may be a bit more... lethal than you're looking for. It's very tricky to judge the results of these kinds of pediatric surveys on effects such as obesity, increased or decreased intelligence, etc, because so many other confounding factors are present. As such, at least for this study, the binary approach of 'dead' or 'not dead' shows that there's no increased risk of really, really bad outcomes as a result of ultrasounds. And that's using late 1980s-early 1990's imaging tech.
As such, in 2002, Marinac-Dabic et al called for a more inclusive definition of 'adverse outcomes':
However, there have been some reports that there may be a relation between prenatal ultrasound exposure and adverse outcome. Some of the reported effects include growth restriction, delayed speech, dyslexia, and non-right-handedness associated with ultrasound exposure. Continued research is needed to evaluate the potential adverse effects of ultrasound exposure during pregnancy.
I tend not to think that left-handedness is as bad as dyslexia or growth restriction, given that Presidents of the United States tend to be either right or left handed, but the other charges are definitely worth investigating.
As such, in 2009, the WHO published a meta-analysis of the literature to determine if there were any adverse effects for the practice. They concluded:
Ultrasonography in pregnancy was not associated with adverse maternal or perinatal outcome, impaired physical or neurological development, increased risk for malignancy in childhood, subnormal intellectual performance or mental diseases. According to the available clinical trials, there was a weak association between exposure to ultrasonography and non-right handedness in boys (odds ratio 1.26; 95% CI, 1.03–1.54).
tl;dr: In effect, by the best judgement we have, ultrasonic imaging is a safe screening method, and has no adverse effects on the baby.