You can use rowSums to check if any element of a row is not finite. 
DT[is.finite(rowSums(DT))]
OR you can use the fact that Inf * 0 is NA and use complete.cases
DT[complete.cases(DT*0)]
Some benchmarking shows that the rowSums is fastest for smaller datasets and complete.cases is the fastest solution for larger datasets. 
require(microbenchmark)
microbenchmark(
  DT[is.finite(rowSums(DT))]
  ,
  DT[complete.cases(DT*0)]
  ,
  DT[DT[, Reduce('&', lapply(.SD, is.finite))]]
)
##
## nrow(DT) = 3000
## Unit: microseconds                                          
##                                          expr       min       lq      mean    median       uq      max neval cld
##                     DT[is.finite(rowSums(DT))]  786.797  839.235  864.0215  852.8465  884.756 1021.988   100 a  
##                     DT[complete.cases(DT * 0)] 1265.658 1326.575 1363.3985 1350.0055 1386.377 1898.040   100   c
##  DT[DT[, Reduce("&", lapply(.SD, is.finite))]] 1220.137 1275.030 1319.6226 1308.0555 1348.443 1624.023   100  b 
##
## nrow(DT) = 300000
## Unit: milliseconds
##                                           expr       min        lq      mean   median       uq      max neval cld
##                     DT[is.finite(rowSums(DT))] 21.617935 22.687452 26.698070 25.75765 26.07942 87.56290   100   c
##                     DT[complete.cases(DT * 0)]  7.209252  7.567393  9.908503 10.17569 10.37473 71.31375   100 a  
##  DT[DT[, Reduce("&", lapply(.SD, is.finite))]] 11.786773 12.647652 14.128624 14.78512 15.05089 15.39542   100  b