The literature on the toxic effects of AZT is voluminous. We have provided a survey detailing the shocking side effects (including death) at rethinkingaids.com/quotes/azt.html.
The Gallo document claims that AZT does not kill cells indiscriminately but then, buried in a footnote, describes accurately that AZT acts as an analog of the DNA-component, thymidine. This would mean that HIV can stop DNA synthesis, and thus cell division.
However, there is a scientific research review published in 1999  shows that AZT is not triphosphorylated to a significant degree and therefore cannot have the claimed mode of action. Triphosphorylation is necessary to activate AZT and allow its incorporation into DNA.
The fact that AZT cannot interfere with viral transcription does not mean that it cannot have side effects. The fact that it has been noted by many authors that AZT does damage mitochondria, cellular energy-regulating organelles that have their own DNA and replicate independently, means that it is interfering with DNA synthesis, but not in the way claimed by the Gallo document.
It is particularly shocking that a drug that interferes with cellular and mitochondrial DNA synthesis should be prescribed to pregnant women and children. One paper published in 2003 recorded that All the children with established or possible mitochondriopathy [mitochondrial damage] diagnosed in this study had been exposed to antiretroviral drugs. One of these children was treated with zidovudine [AZT] only during the prenatal period and received no treatment after birth
For the other children, the treatment was administered in the pre, per- and post-partum periods. It was zidovudine alone in five cases, a combination of zidovudine-lamivudine in 14 cases and another combination in one. 20 of the mothers received zidovudine by intravenous perfusion during labor. 
The side effects of AZT lead to real, measurable clinical damage. Several studies have recorded conclusions similar to Comparison of HIV-1-infected children whose mothers were treated with ZDV [AZT] with children whose mothers were not treated showed that the former group had a [1.8 times] higher probability of developing severe disease or severe immune suppression [2.4 times higher risk] and a lower survival (72.2% versus 81.0%). 
It is not surprising to read papers with titles like AZT is a Genotoxic Transplacental Carcinogen in Animal Models . Translated, this title means that, in monkeys and mice, AZT damages DNA, causes cancer, and crosses the placenta from mother to her offspring.
The Gallo document closes by stating AZT therefore remains a highly useful drug for HIV therapy. This has been shown in clinical trials and cohort analyses as demonstrated by several references in our endnotes. They do not specify what those references are.