Factual error: In 1999 when April is filming inside the research facility, you can see her video camera displaying Bluetooth, which wasn't available in cameras until 2002.
Factual error: After the sewer invasion, April watches the three captured turtles drive away, then she turns to go to Splinter. Shortly thereafter, the computer screen shows GPS tracking the turtles at a location easily over an hour away from Manhattan. Likewise, the estate is referred to as being just forty minutes away from the city. (00:56:10 - 00:58:50)
Answer: While never really adressed, the most popular fan theories suggest that either: 1. Splinter manufactured the weapons with materials he found in the sewers or 2. Splinter scavenged for the weapons at a local dump or 3. They were ordered online (only applies to the 2014 version). Fans admit these explanations are kind of a stretch but certain scenes across movies and/or series lend credibility to one explanation or the other. 1. They seem to know how to improve or even craft their weapons meaning that someone taught them (Splinter). 2. They seem to be troubled when a weapon goes missing or breaks meaning they have limited access to spares. 3. Money doesn't seem to be an issue considering all the pizza that is consumed (in some cases the Turtles have been seen holding down jobs like tech support or birthday party mascot). The original purchase could've been made with money scavanged in the sewers and delivered to a P.O. box Source: https://tinyurl.com/y6kbxhlq.